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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 9 and 15.</p>

4 <h2>What is the GCF of 9 and 15?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>9 and 15 is 3. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.</p>

6 <h2>How to find the GCF of 9 and 15?</h2>

7 <p>To find the GCF of 9 and 15, a few methods are described below</p>

8 <ul><li>Listing Factors</li>

9 <li>Prime Factorization</li>

10 <li>Long Division Method / by Euclidean Algorithm</li>

11 </ul><h2>GCF of 9 and 15 by Using Listing of factors</h2>

12 <p>Steps to find the GCF of 9 and 15 using the listing of<a>factors</a></p>

13 <p><strong>Step 1:</strong>Firstly, list the factors of each number</p>

14 <p>Factors of 9 = 1, 3, 9.</p>

15 <p>Factors of 15 = 1, 3, 5, 15.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 9 and 15: 1, 3.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor</p>

18 <p>The largest factor that both numbers have is 3.</p>

19 <p>The GCF of 9 and 15 is 3.</p>

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22 <h2>GCF of 9 and 15 Using Prime Factorization</h2>

21 <h2>GCF of 9 and 15 Using Prime Factorization</h2>

23 <p>To find the GCF of 9 and 15 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 9 and 15 using the Prime Factorization Method, follow these steps:</p>

24 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

23 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

25 <p>Prime Factors of 9: 9 = 3 x 3 = 3²</p>

24 <p>Prime Factors of 9: 9 = 3 x 3 = 3²</p>

26 <p>Prime Factors of 15: 15 = 3 x 5</p>

25 <p>Prime Factors of 15: 15 = 3 x 5</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors</p>

28 <p>The common prime factor is: 3</p>

27 <p>The common prime factor is: 3</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

30 <p>The GCF of 9 and 15 is 3.</p>

29 <p>The GCF of 9 and 15 is 3.</p>

31 <h2>GCF of 9 and 15 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 9 and 15 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 9 and 15 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 9 and 15 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

33 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

32 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

34 <p>Here, divide 15 by 9 15 ÷ 9 = 1 (<a>quotient</a>),</p>

33 <p>Here, divide 15 by 9 15 ÷ 9 = 1 (<a>quotient</a>),</p>

35 <p>The<a>remainder</a>is calculated as 15 - (9×1) = 6</p>

34 <p>The<a>remainder</a>is calculated as 15 - (9×1) = 6</p>

36 <p>The remainder is 6, not zero, so continue the process</p>

35 <p>The remainder is 6, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (9) by the previous remainder (6)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (9) by the previous remainder (6)</p>

38 <p>Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 - (6×1) = 3</p>

37 <p>Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 - (6×1) = 3</p>

39 <p><strong>Step 3:</strong>Now divide the previous divisor (6) by the previous remainder (3)</p>

38 <p><strong>Step 3:</strong>Now divide the previous divisor (6) by the previous remainder (3)</p>

40 <p>Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

39 <p>Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

41 <p>The remainder is zero, the divisor will become the GCF.</p>

40 <p>The remainder is zero, the divisor will become the GCF.</p>

42 <p>The GCF of 9 and 15 is 3.</p>

41 <p>The GCF of 9 and 15 is 3.</p>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 15</h2>

42 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 15</h2>

44 <p>Finding GCF of 9 and 15 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

43 <p>Finding GCF of 9 and 15 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

45 <h3>Problem 1</h3>

44 <h3>Problem 1</h3>

46 <p>A gardener has 9 rose bushes and 15 tulip bulbs. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

45 <p>A gardener has 9 rose bushes and 15 tulip bulbs. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

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

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

48 <p>We should find GCF of 9 and 15 GCF of 9 and 15 is 3.</p>

47 <p>We should find GCF of 9 and 15 GCF of 9 and 15 is 3.</p>

49 <p>There are 3 equal groups 9 ÷ 3 = 3 15 ÷ 3 = 5</p>

48 <p>There are 3 equal groups 9 ÷ 3 = 3 15 ÷ 3 = 5</p>

50 <p>There will be 3 groups, and each group gets 3 rose bushes and 5 tulip bulbs.</p>

49 <p>There will be 3 groups, and each group gets 3 rose bushes and 5 tulip bulbs.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>As the GCF of 9 and 15 is 3, the gardener can make 3 groups. Now divide 9 and 15 by 3.</p>

51 <p>As the GCF of 9 and 15 is 3, the gardener can make 3 groups. Now divide 9 and 15 by 3.</p>

53 <p>Each group gets 3 rose bushes and 5 tulip bulbs.</p>

52 <p>Each group gets 3 rose bushes and 5 tulip bulbs.</p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 2</h3>

54 <h3>Problem 2</h3>

56 <p>A chef has 9 red apples and 15 green apples. He wants to arrange them in rows with the same number of apples in each row, using the largest possible number of apples per row. How many apples will be in each row?</p>

55 <p>A chef has 9 red apples and 15 green apples. He wants to arrange them in rows with the same number of apples in each row, using the largest possible number of apples per row. How many apples will be in each row?</p>

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

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

58 <p>GCF of 9 and 15 is 3.</p>

57 <p>GCF of 9 and 15 is 3.</p>

59 <p>So each row will have 3 apples.</p>

58 <p>So each row will have 3 apples.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>There are 9 red and 15 green apples.</p>

60 <p>There are 9 red and 15 green apples.</p>

62 <p>To find the total number of apples in each row, we should find the GCF of 9 and 15.</p>

61 <p>To find the total number of apples in each row, we should find the GCF of 9 and 15.</p>

63 <p>There will be 3 apples in each row.</p>

62 <p>There will be 3 apples in each row.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 3</h3>

64 <h3>Problem 3</h3>

66 <p>A tailor has 9 meters of red fabric and 15 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

65 <p>A tailor has 9 meters of red fabric and 15 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

68 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 15</p>

67 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 15</p>

69 <p>The GCF of 9 and 15 is 3.</p>

68 <p>The GCF of 9 and 15 is 3.</p>

70 <p>The fabric is 3 meters long.</p>

69 <p>The fabric is 3 meters long.</p>

71 <h3>Explanation</h3>

70 <h3>Explanation</h3>

72 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 9 and 15, which is 3.</p>

71 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 9 and 15, which is 3.</p>

73 <p>The length of each piece of fabric will be 3 meters.</p>

72 <p>The length of each piece of fabric will be 3 meters.</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h3>Problem 4</h3>

74 <h3>Problem 4</h3>

76 <p>A carpenter has two wooden planks, one 9 cm long and the other 15 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?</p>

75 <p>A carpenter has two wooden planks, one 9 cm long and the other 15 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?</p>

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

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

78 <p>The carpenter needs the longest piece of wood GCF of 9 and 15 is 3.</p>

77 <p>The carpenter needs the longest piece of wood GCF of 9 and 15 is 3.</p>

79 <p>The longest length of each piece is 3 cm.</p>

78 <p>The longest length of each piece is 3 cm.</p>

80 <h3>Explanation</h3>

79 <h3>Explanation</h3>

81 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 15 cm respectively, we have to find the GCF of 9 and 15, which is 3 cm.</p>

80 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 15 cm respectively, we have to find the GCF of 9 and 15, which is 3 cm.</p>

82 <p>The longest length of each piece is 3 cm.</p>

81 <p>The longest length of each piece is 3 cm.</p>

83 <p>Well explained 👍</p>

82 <p>Well explained 👍</p>

84 <h3>Problem 5</h3>

83 <h3>Problem 5</h3>

85 <p>If the GCF of 9 and ‘b’ is 3, and the LCM is 45. Find ‘b’.</p>

84 <p>If the GCF of 9 and ‘b’ is 3, and the LCM is 45. Find ‘b’.</p>

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

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

87 <p>The value of ‘b’ is 15.</p>

86 <p>The value of ‘b’ is 15.</p>

88 <h3>Explanation</h3>

87 <h3>Explanation</h3>

89 <p>GCF x LCM = product of the numbers 3 × 45 = 9 × b</p>

88 <p>GCF x LCM = product of the numbers 3 × 45 = 9 × b</p>

90 <p>135 = 9b</p>

89 <p>135 = 9b</p>

91 <p>b = 135 ÷ 9 = 15</p>

90 <p>b = 135 ÷ 9 = 15</p>

92 <p>Well explained 👍</p>

91 <p>Well explained 👍</p>

93 <h2>FAQs on the Greatest Common Factor of 9 and 15</h2>

92 <h2>FAQs on the Greatest Common Factor of 9 and 15</h2>

94 <h3>1.What is the LCM of 9 and 15?</h3>

93 <h3>1.What is the LCM of 9 and 15?</h3>

95 <p>The LCM of 9 and 15 is 45.</p>

94 <p>The LCM of 9 and 15 is 45.</p>

96 <h3>2.Is 9 divisible by 3?</h3>

95 <h3>2.Is 9 divisible by 3?</h3>

97 <p>Yes, 9 is divisible by 3 because the<a>sum</a>of its digits is divisible by 3.</p>

96 <p>Yes, 9 is divisible by 3 because the<a>sum</a>of its digits is divisible by 3.</p>

98 <h3>3.What will be the GCF of any two prime numbers?</h3>

97 <h3>3.What will be the GCF of any two prime numbers?</h3>

99 <p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>

98 <p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>

100 <h3>4.What is the prime factorization of 15?</h3>

99 <h3>4.What is the prime factorization of 15?</h3>

101 <p>The prime factorization of 15 is 3 x 5.</p>

100 <p>The prime factorization of 15 is 3 x 5.</p>

102 <h3>5.Are 9 and 15 prime numbers?</h3>

101 <h3>5.Are 9 and 15 prime numbers?</h3>

103 <p>No, 9 and 15 are not prime numbers because both of them have more than two factors.</p>

102 <p>No, 9 and 15 are not prime numbers because both of them have more than two factors.</p>

104 <h2>Important Glossaries for GCF of 9 and 15</h2>

103 <h2>Important Glossaries for GCF of 9 and 15</h2>

105 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

104 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

106 <li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.</li>

105 <li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.</li>

107 <li><strong>Prime Factors:</strong>These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 15 are 3 and 5.</li>

106 <li><strong>Prime Factors:</strong>These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 15 are 3 and 5.</li>

108 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.</li>

107 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.</li>

109 <li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 15 is 3, as it is their largest common factor that divides the numbers completely.</li>

108 <li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 15 is 3, as it is their largest common factor that divides the numbers completely.</li>

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

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

111 <p>▶</p>

110 <p>▶</p>

112 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h2>Hiralee Lalitkumar Makwana</h2>

113 <h3>About the Author</h3>

112 <h3>About the Author</h3>

114 <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>

113 <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>

115 <h3>Fun Fact</h3>

114 <h3>Fun Fact</h3>

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

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