Rivalry2

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2 <p>Last updated on<strong>December 2, 2025</strong></p>

3 <p>Imagine you are taking a number and multiplying it by every whole number before it until you reach 1; that result is the factorial. Factorials help you discover how many ways things can be arranged. In this article, we will explore the concept in detail.</p>

4 <h2>What is a Factorial?</h2>

5 <p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

6 <p>▶</p>

7 <p>Factorial is the way<a>of</a>multiplying a<a>number</a>by every<a>whole number</a>below it, all the way down to 1. We show that a factorial is denoted by the<a>symbol</a>‘!’, which is the one above the number 1 on a computer keyboard. When we say n! (read as “n factorial”), which means we multiply all the<a>positive integers</a>from 1 up to n.</p>

8 <p>So, the factorial definition can be written as:</p>

9 <p>\(\text{n! = 1 × 2 × 3 × ... × n or, }\\[1em] \text{n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1}\)</p>

10 <p><strong>Example:</strong></p>

11 <p>Find the value of 5! (5 factorial).</p>

12 <p><strong>Answer</strong></p>

13 <p>\(5! = 5 × 4 × 3 × 2 × 1\)</p>

14 <p>5! = 120</p>

15 <p>So, the value of 5! is 120.</p>

16 <h2>Formula for Factorial</h2>

17 <p>The factorial of a number n is found by multiplying all the whole numbers from n down to 1. The<a>formula</a>is:</p>

18 <p>For any whole number n ≥ 1, the factorial can also be written using the<a>product</a>notation:</p>

19 <p>From these formulas, we can get a useful pattern called the recurrence<a>relation</a>, which shows how each factorial is built using the previous one:</p>

20 <p>n! = n × (n - 1)!</p>

21 <p>This means you can find the larger factorial by multiplying the number n by the factorial of the number just before it.</p>

22 <h2>Factorial Table</h2>

23 <p>The factorial table showcases the numbers and their factorial values. As seen below, we determine the factorial of a given number by multiplying it by the factorial of the preceding number. <a>i</a>.e., \(n! = n \times (n-1) \times (n-2) \times \dots \times 1 \)</p>

24 <p>For example, to find the factorial of 6, multiply 6 by the factorial of 5:</p>

25 <p>\(6! = 6 \times 120 = 720 \quad (5! = 120) \)</p>

26 <p>Similarly, the factorial of 7:</p>

27 <p>\(7! = 7 \times 720 = 5040 \quad (6! = 720) \)</p>

28 <strong>n Factorial</strong><strong>\(\mathbf{n (n-1) (n-2) \dots 1 }\)</strong><strong>\(\mathbf{n! = n \times (n-1)! }\)</strong><strong>Result</strong><p>1 Factorial</p>

29 1 1 1 2 Factorial \(2 × 1\) \(= 2 × 1!\) \(= 2\)<p>3 Factorial</p>

30 \(3 × 2 × 1\) \(= 3 × 2!\) \(= 6\) 4 Factorial \(4 × 3 × 2 × 1\) \(= 4 ×3 !\) \(= 24\)<p>5 Factorial</p>

31 \(5 × 4 × 3 × 2 × 1\) \(= 5 × 4!\) \(= 120\)<h3>Explore Our Programs</h3>

32 - <p>No Courses Available</p>

33 <h2>What is the Subfactorial of a Number?</h2>

32 <h2>What is the Subfactorial of a Number?</h2>

34 <p>A subfactorial of a number is written as !n. It tells us how many ways we can rearrange the n objects so that none of them stay in their original position. In other words, it counts the number of derangements, shuffled arrangements where every item is moves to a different place.</p>

33 <p>A subfactorial of a number is written as !n. It tells us how many ways we can rearrange the n objects so that none of them stay in their original position. In other words, it counts the number of derangements, shuffled arrangements where every item is moves to a different place.</p>

35 <p>The formula for finding the subfactorial of n is: </p>

34 <p>The formula for finding the subfactorial of n is: </p>

36 <p>\(!n = n! \sum_{k=0}^{n} \frac{(-1)^k}{k!}\)</p>

35 <p>\(!n = n! \sum_{k=0}^{n} \frac{(-1)^k}{k!}\)</p>

37 <h2>Factorial of 0 (Zero)</h2>

36 <h2>Factorial of 0 (Zero)</h2>

38 <p>It is easy to assume that the factorial of 0 is 0, but this is incorrect. The factorial of 0 is 1 which can be written as:</p>

37 <p>It is easy to assume that the factorial of 0 is 0, but this is incorrect. The factorial of 0 is 1 which can be written as:</p>

39 <p>\(0! = 1\).</p>

38 <p>\(0! = 1\).</p>

40 <p>Factorials often follow a pattern:</p>

39 <p>Factorials often follow a pattern:</p>

41 <p>\(1! = 1\)</p>

40 <p>\(1! = 1\)</p>

42 <p>\(2! = 2 × 1 = 2\)</p>

41 <p>\(2! = 2 × 1 = 2\)</p>

43 <p>\(3! = 3 × 2 × 1 = 3 × 2! = 6 \)</p>

42 <p>\(3! = 3 × 2 × 1 = 3 × 2! = 6 \)</p>

44 <p>\(4! = 4 × 3 × 2 × 1 = 4 × 3! = 24\)</p>

43 <p>\(4! = 4 × 3 × 2 × 1 = 4 × 3! = 24\)</p>

45 <p>To understand the zero factorial better, let’s look at the following method: </p>

44 <p>To understand the zero factorial better, let’s look at the following method: </p>

46 <p>We find \(3!\) by dividing the factorial of the succeeding number by that number:</p>

45 <p>We find \(3!\) by dividing the factorial of the succeeding number by that number:</p>

47 <p>\(3! = \frac{4!}{4} \)</p>

46 <p>\(3! = \frac{4!}{4} \)</p>

48 <p>\(2! = \frac{3!}{3} \)</p>

47 <p>\(2! = \frac{3!}{3} \)</p>

49 <p>\(1! = \frac{2!}{2} \)</p>

48 <p>\(1! = \frac{2!}{2} \)</p>

50 <p>\(0! = \frac{1!}{1} \)</p>

49 <p>\(0! = \frac{1!}{1} \)</p>

51 <h2>Factorial of n</h2>

50 <h2>Factorial of n</h2>

52 <p>The factorial of a number n is the product of the first n natural<a>integers</a>can be expressed as:</p>

51 <p>The factorial of a number n is the product of the first n natural<a>integers</a>can be expressed as:</p>

53 <p>\(n! = n × (n -1) × (n - 2) ×… × 3 × 2 × 1\). </p>

52 <p>\(n! = n × (n -1) × (n - 2) ×… × 3 × 2 × 1\). </p>

54 <p>The n factorial can be mathematically represented as the product of the given number by the factorial of the preceding number:</p>

53 <p>The n factorial can be mathematically represented as the product of the given number by the factorial of the preceding number:</p>

55 <p>\(n! = n × (n - 1)!\)</p>

54 <p>\(n! = n × (n - 1)!\)</p>

56 <h2>Factorial of Negative Numbers</h2>

55 <h2>Factorial of Negative Numbers</h2>

57 <p>There is a common misconception that factorials include<a>negative numbers</a>. We will now learn why factorials are undefined for negative numbers. Here, we start with the factorial of 3.</p>

56 <p>There is a common misconception that factorials include<a>negative numbers</a>. We will now learn why factorials are undefined for negative numbers. Here, we start with the factorial of 3.</p>

58 <p>\(3! = 3 \times 2 \times 1 = 6 \)</p>

57 <p>\(3! = 3 \times 2 \times 1 = 6 \)</p>

59 <p>\(2! = \frac{3!}{3} = \frac{6}{3} = 2 \)</p>

58 <p>\(2! = \frac{3!}{3} = \frac{6}{3} = 2 \)</p>

60 <p>\(1! = \frac{2!}{2} = \frac{2}{2} = 1 \)</p>

59 <p>\(1! = \frac{2!}{2} = \frac{2}{2} = 1 \)</p>

61 <p>\(0! = \frac{1!}{1} = \frac{1}{1} = 1 \)</p>

60 <p>\(0! = \frac{1!}{1} = \frac{1}{1} = 1 \)</p>

62 <p>\((-1)! = 0! ÷ 0 = 1 ÷ 0\) (undefined, since<a>division by zero</a>is impossible).</p>

61 <p>\((-1)! = 0! ÷ 0 = 1 ÷ 0\) (undefined, since<a>division by zero</a>is impossible).</p>

63 <p>Thus, factorials are undefined for negative numbers. </p>

62 <p>Thus, factorials are undefined for negative numbers. </p>

64 <h2>How to Calculate Factorial of Numbers</h2>

63 <h2>How to Calculate Factorial of Numbers</h2>

65 <p>As we have learned, the factorials of n are represented as n! And is determined using the formula \(n! = n × (n - 1)!\) </p>

64 <p>As we have learned, the factorials of n are represented as n! And is determined using the formula \(n! = n × (n - 1)!\) </p>

66 <p>If \(7! = 5,040\), then \(8! = 8 × 7! = 8 × 5,040 = 40,320.\)</p>

65 <p>If \(7! = 5,040\), then \(8! = 8 × 7! = 8 × 5,040 = 40,320.\)</p>

67 <p>The table below shows the factorials of the first 15 numbers:</p>

66 <p>The table below shows the factorials of the first 15 numbers:</p>

68 <strong>n Factorial</strong><strong>Value</strong>1 Factorial 1 2 Factorial 2 3 Factorial 6 4 Factorial 24 5 Factorial 120 6 Factorial 720 7 Factorial 5040 8 Factorial 40320 9 Factorial 362880 10 Factorial 3628800 11 Factorial 39916800 12 Factorial 479001600 13 Factorial 6227020800 14 Factorial 87178291200 15 Factorial 1307674368000<h2>Tips and Tricks to Master Factorial</h2>

67 <strong>n Factorial</strong><strong>Value</strong>1 Factorial 1 2 Factorial 2 3 Factorial 6 4 Factorial 24 5 Factorial 120 6 Factorial 720 7 Factorial 5040 8 Factorial 40320 9 Factorial 362880 10 Factorial 3628800 11 Factorial 39916800 12 Factorial 479001600 13 Factorial 6227020800 14 Factorial 87178291200 15 Factorial 1307674368000<h2>Tips and Tricks to Master Factorial</h2>

69 <p>For developing a deeper understanding of factorials, follow these tips and tricks given below: </p>

68 <p>For developing a deeper understanding of factorials, follow these tips and tricks given below: </p>

70 <ul><li>Start by recognizing that a factorial is the product of all positive integers up to a given number. </li>

69 <ul><li>Start by recognizing that a factorial is the product of all positive integers up to a given number. </li>

71 <li>Remember the recursive relationship \(n! = n × (n - 1)!\). This means you can compute larger factorials by building upon smaller ones. </li>

70 <li>Remember the recursive relationship \(n! = n × (n - 1)!\). This means you can compute larger factorials by building upon smaller ones. </li>

72 <li>When dividing factorials, cancel common<a>terms</a>to simplify calculations. </li>

71 <li>When dividing factorials, cancel common<a>terms</a>to simplify calculations. </li>

73 <li>Many<a>calculators</a>have a factorial function (\(n!\)). Utilize this feature to quickly compute factorials without manual<a>multiplication</a>. </li>

72 <li>Many<a>calculators</a>have a factorial function (\(n!\)). Utilize this feature to quickly compute factorials without manual<a>multiplication</a>. </li>

74 <li>Factorials grow rapidly and from them try to recognize the patterns. For example, \(10! = 3,628,800\). </li>

73 <li>Factorials grow rapidly and from them try to recognize the patterns. For example, \(10! = 3,628,800\). </li>

75 <li>Explain that the factorial notation (n!) means multiplying all positive integers from 'n' to '1'. </li>

74 <li>Explain that the factorial notation (n!) means multiplying all positive integers from 'n' to '1'. </li>

76 <li>Start with 1!, 2!, 3 Factorial (3!), 4!. Small numbers build confidence before the larger ones. </li>

75 <li>Start with 1!, 2!, 3 Factorial (3!), 4!. Small numbers build confidence before the larger ones. </li>

77 <li>Use the fundamental factorial rule: n! = n × (n - 1)!. This shows how each factorial uses the previous one. </li>

76 <li>Use the fundamental factorial rule: n! = n × (n - 1)!. This shows how each factorial uses the previous one. </li>

78 <li>Most calculators (and online tools) have a factorial calculator function. Let children try the manual steps first, then verify using the tool.</li>

77 <li>Most calculators (and online tools) have a factorial calculator function. Let children try the manual steps first, then verify using the tool.</li>

79 </ul><h2>Common Mistakes and How to Avoid Them in Factorials</h2>

78 </ul><h2>Common Mistakes and How to Avoid Them in Factorials</h2>

80 <p>The concept of factorial is an important theory and has several applications. However, students might make mistakes when solving problems related to it. Here are a few common mistakes and the easy ways to avoid them:</p>

79 <p>The concept of factorial is an important theory and has several applications. However, students might make mistakes when solving problems related to it. Here are a few common mistakes and the easy ways to avoid them:</p>

81 <h2>Real-World Applications of Factorial</h2>

80 <h2>Real-World Applications of Factorial</h2>

82 <p>Factorials are of immense significance in various real-life situations. Let’s now look at a few such examples:</p>

81 <p>Factorials are of immense significance in various real-life situations. Let’s now look at a few such examples:</p>

83 <ul><li>Factorials play a vital role in determining the total number of ways things can be arranged, such as seating arrangements and the arrangement of books on a shelf. </li>

82 <ul><li>Factorials play a vital role in determining the total number of ways things can be arranged, such as seating arrangements and the arrangement of books on a shelf. </li>

84 <li>They can be applied to calculate the total possible outcomes in events influenced by<a>probability</a>, such as outcomes in lotteries. </li>

83 <li>They can be applied to calculate the total possible outcomes in events influenced by<a>probability</a>, such as outcomes in lotteries. </li>

85 <li>In scientific scenarios, they are used for gene arrangements or in DNA sequencing. </li>

84 <li>In scientific scenarios, they are used for gene arrangements or in DNA sequencing. </li>

86 <li>In sports, they are used in planning and arranging tournaments. </li>

85 <li>In sports, they are used in planning and arranging tournaments. </li>

87 <li>They are used in finance to evaluate risk<a>factors</a>by analyzing possible outcomes in stock markets.</li>

86 <li>They are used in finance to evaluate risk<a>factors</a>by analyzing possible outcomes in stock markets.</li>

88 </ul><h3>Problem 1</h3>

87 </ul><h3>Problem 1</h3>

89 <p>Determine the value of (5! ÷ 4! × 3!).</p>

88 <p>Determine the value of (5! ÷ 4! × 3!).</p>

90 <p>Okay, lets begin</p>

89 <p>Okay, lets begin</p>

91 <p>\((5! ÷ 4! × 3!) = 30\)</p>

90 <p>\((5! ÷ 4! × 3!) = 30\)</p>

92 <h3>Explanation</h3>

91 <h3>Explanation</h3>

93 <p>Let’s first calculate the factorials of 5, 4, and 3 separately:</p>

92 <p>Let’s first calculate the factorials of 5, 4, and 3 separately:</p>

94 <p>\(5! = 5 × 4 × 3 × 2 × 1 = 120\)</p>

93 <p>\(5! = 5 × 4 × 3 × 2 × 1 = 120\)</p>

95 <p>\(4! = 4 × 3 × 2 × 1 = 24\)</p>

94 <p>\(4! = 4 × 3 × 2 × 1 = 24\)</p>

96 <p>\(3! = 3 × 2 × 1= 6\)</p>

95 <p>\(3! = 3 × 2 × 1= 6\)</p>

97 <p>We now substitute these values:</p>

96 <p>We now substitute these values:</p>

98 <p>\((5! ÷ 4! × 3!) = (120 ÷ 24) × 6\)</p>

97 <p>\((5! ÷ 4! × 3!) = (120 ÷ 24) × 6\)</p>

99 <p>\(= 5 × 6\)</p>

98 <p>\(= 5 × 6\)</p>

100 <p>\(= 30\)</p>

99 <p>\(= 30\)</p>

101 <p>Well explained 👍</p>

100 <p>Well explained 👍</p>

102 <h3>Problem 2</h3>

101 <h3>Problem 2</h3>

103 <p>Alex has 8 different books and wants to organize them on a shelf. In how many possible ways he can organize these books?</p>

102 <p>Alex has 8 different books and wants to organize them on a shelf. In how many possible ways he can organize these books?</p>

104 <p>Okay, lets begin</p>

103 <p>Okay, lets begin</p>

105 <p>Alex can organize the books in 40,320 different ways.</p>

104 <p>Alex can organize the books in 40,320 different ways.</p>

106 <h3>Explanation</h3>

105 <h3>Explanation</h3>

107 <p>To find the possible ways in which Alex can organize the books, we use the formula:</p>

106 <p>To find the possible ways in which Alex can organize the books, we use the formula:</p>

108 <p>\(n! = n (n -1) (n - 2)... 3 × 2 × 1\)</p>

107 <p>\(n! = n (n -1) (n - 2)... 3 × 2 × 1\)</p>

109 <p>Given that, there are 8 books:</p>

108 <p>Given that, there are 8 books:</p>

110 <p>So the total number of arrangements is:</p>

109 <p>So the total number of arrangements is:</p>

111 <p>\(8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1\)</p>

110 <p>\(8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1\)</p>

112 <p>\(= 40,320\)</p>

111 <p>\(= 40,320\)</p>

113 <p>Therefore, Alex can organize the books in 40,320 different ways.</p>

112 <p>Therefore, Alex can organize the books in 40,320 different ways.</p>

114 <p>Well explained 👍</p>

113 <p>Well explained 👍</p>

115 <h3>Problem 3</h3>

114 <h3>Problem 3</h3>

116 <p>How many different ways can the letters in the word "EDUCATION" be arranged if all letters are used?</p>

115 <p>How many different ways can the letters in the word "EDUCATION" be arranged if all letters are used?</p>

117 <p>Okay, lets begin</p>

116 <p>Okay, lets begin</p>

118 <p>The word“ EDUCATION” can be arranged in 362,880 different ways.</p>

117 <p>The word“ EDUCATION” can be arranged in 362,880 different ways.</p>

119 <h3>Explanation</h3>

118 <h3>Explanation</h3>

120 <p>All the letters in the given word are unique, so the total number of ways to arrange them is:</p>

119 <p>All the letters in the given word are unique, so the total number of ways to arrange them is:</p>

121 <p>\(n! = n (n -1) (n - 2)... 3 × 2 × 1\)</p>

120 <p>\(n! = n (n -1) (n - 2)... 3 × 2 × 1\)</p>

122 <p>\(9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880\)</p>

121 <p>\(9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880\)</p>

123 <p>So, there are 362,880 different arrangements.</p>

122 <p>So, there are 362,880 different arrangements.</p>

124 <p>Well explained 👍</p>

123 <p>Well explained 👍</p>

125 <h3>Problem 4</h3>

124 <h3>Problem 4</h3>

126 <p>Determine the value of 4!10!</p>

125 <p>Determine the value of 4!10!</p>

127 <p>Okay, lets begin</p>

126 <p>Okay, lets begin</p>

128 <p>\(4! × 10! = 87,091,200\)</p>

127 <p>\(4! × 10! = 87,091,200\)</p>

129 <h3>Explanation</h3>

128 <h3>Explanation</h3>

130 <p>Let’s first calculate the factorials of 4 and 10 separately:</p>

129 <p>Let’s first calculate the factorials of 4 and 10 separately:</p>

131 <p>\(4! = 4 × 3 × 2 × 1 = 24\)</p>

130 <p>\(4! = 4 × 3 × 2 × 1 = 24\)</p>

132 <p>\(10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800\)</p>

131 <p>\(10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800\)</p>

133 <p>We’ll now multiply the factorials:</p>

132 <p>We’ll now multiply the factorials:</p>

134 <p>\( 4!10! = 24 × 3,628,800 = 87,091,200\)</p>

133 <p>\( 4!10! = 24 × 3,628,800 = 87,091,200\)</p>

135 <p>Well explained 👍</p>

134 <p>Well explained 👍</p>

136 <h3>Problem 5</h3>

135 <h3>Problem 5</h3>

137 <p>Find the value of (12! - 8!)</p>

136 <p>Find the value of (12! - 8!)</p>

138 <p>Okay, lets begin</p>

137 <p>Okay, lets begin</p>

139 <p>\(12! - 8! = 479,001,600 - 40,320 = 478,961,280.\)</p>

138 <p>\(12! - 8! = 479,001,600 - 40,320 = 478,961,280.\)</p>

140 <h3>Explanation</h3>

139 <h3>Explanation</h3>

141 <p>We will first find the factorials of 12 and 8 separately:</p>

140 <p>We will first find the factorials of 12 and 8 separately:</p>

142 <p>\(12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1\)</p>

141 <p>\(12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1\)</p>

143 <p>\(= 479,001,600\)</p>

142 <p>\(= 479,001,600\)</p>

144 <p>\(8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320\)</p>

143 <p>\(8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320\)</p>

145 <p>Now, substitute these values:</p>

144 <p>Now, substitute these values:</p>

146 <p>\(12! - 8! = 479,001,600 - 40,320\)</p>

145 <p>\(12! - 8! = 479,001,600 - 40,320\)</p>

147 <p>\(= 478,961,280\)</p>

146 <p>\(= 478,961,280\)</p>

148 <p>Well explained 👍</p>

147 <p>Well explained 👍</p>

149 <h2>FAQs on Factorials</h2>

148 <h2>FAQs on Factorials</h2>

150 <h3>1.What do you mean by a factorial?</h3>

149 <h3>1.What do you mean by a factorial?</h3>

151 <p>A factorial is a function that multiplies a number by every whole number lower than the number, until 1. We use the symbol “!” to denote the factorial. </p>

150 <p>A factorial is a function that multiplies a number by every whole number lower than the number, until 1. We use the symbol “!” to denote the factorial. </p>

152 <p>For example, the factorial for 5 is: \(5! = 5 × 4 × 3 × 2 × 1 = 120.\)</p>

151 <p>For example, the factorial for 5 is: \(5! = 5 × 4 × 3 × 2 × 1 = 120.\)</p>

153 <h3>2.Is the value 0! Defined?</h3>

152 <h3>2.Is the value 0! Defined?</h3>

154 <p>Yes, the value of \(0!\) is defined. \( 0!= 1\).</p>

153 <p>Yes, the value of \(0!\) is defined. \( 0!= 1\).</p>

155 <h3>3.Give one real-life example of factorials.</h3>

154 <h3>3.Give one real-life example of factorials.</h3>

156 <p>Factorials are used in determining the total number of arrangements of things like books on a shelf.</p>

155 <p>Factorials are used in determining the total number of arrangements of things like books on a shelf.</p>

157 <h3>4.Can we calculate the factorials for negative numbers?</h3>

156 <h3>4.Can we calculate the factorials for negative numbers?</h3>

158 <p>No, factorials cannot be calculated as they are undefined for negative numbers.</p>

157 <p>No, factorials cannot be calculated as they are undefined for negative numbers.</p>

159 <h2>Hiralee Lalitkumar Makwana</h2>

158 <h2>Hiralee Lalitkumar Makwana</h2>

160 <h3>About the Author</h3>

159 <h3>About the Author</h3>

161 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

160 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

162 <h3>Fun Fact</h3>

161 <h3>Fun Fact</h3>

163 <p>: She loves to read number jokes and games.</p>

162 <p>: She loves to read number jokes and games.</p>