Rivalry2

HTML Diff

1 added 2 removed

Original 2026-01-01

Modified 2026-02-28

1 - <p>119 Learners</p>

1 + <p>150 Learners</p>

2 <p>Last updated on<strong>September 20, 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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 36 and 51.</p>

4 <h2>What is the GCF of 36 and 51?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>36 and 51 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.</p>

6 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 36 and 51?</h2>

8 <p>To find the GCF of 36 and 51, a few methods are described below </p>

9 <ul><li>Listing Factors </li>

10 <li>Prime Factorization </li>

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

12 </ul><h2>GCF of 36 and 51 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 36 and 51 using the listing of<a>factors</a></p>

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

15 <p>Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>

16 <p>Factors of 51 = 1, 3, 17, 51.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 36 and 51: 1, 3.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 3.</p>

19 <p>The GCF of 36 and 51 is 3.</p>

20 <h3>Explore Our Programs</h3>

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

22 <h2>GCF of 36 and 51 Using Prime Factorization</h2>

21 <h2>GCF of 36 and 51 Using Prime Factorization</h2>

23 <p>To find the GCF of 36 and 51 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 36 and 51 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 36: 36 = 2 x 2 x 3 x 3 = 22 x 32</p>

24 <p>Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 22 x 32</p>

26 <p>Prime Factors of 51: 51 = 3 x 17</p>

25 <p>Prime Factors of 51: 51 = 3 x 17</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 3</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 3</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factor 3 = 3.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factor 3 = 3.</p>

29 <p>The Greatest Common Factor of 36 and 51 is 3.</p>

28 <p>The Greatest Common Factor of 36 and 51 is 3.</p>

30 <h2>GCF of 36 and 51 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 36 and 51 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 36 and 51 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 36 and 51 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

33 <p>Here, divide 51 by 36 51 ÷ 36 = 1 (<a>quotient</a>),</p>

32 <p>Here, divide 51 by 36 51 ÷ 36 = 1 (<a>quotient</a>),</p>

34 <p>The<a>remainder</a>is calculated as 51 - (36×1) = 15</p>

33 <p>The<a>remainder</a>is calculated as 51 - (36×1) = 15</p>

35 <p>The remainder is 15, not zero, so continue the process</p>

34 <p>The remainder is 15, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (15)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (15)</p>

37 <p>Divide 36 by 15 36 ÷ 15 = 2 (quotient), remainder = 36 - (15×2) = 6</p>

36 <p>Divide 36 by 15 36 ÷ 15 = 2 (quotient), remainder = 36 - (15×2) = 6</p>

38 <p><strong>Step 3:</strong>Now divide the previous divisor (15) by the previous remainder (6)</p>

37 <p><strong>Step 3:</strong>Now divide the previous divisor (15) by the previous remainder (6)</p>

39 <p>Divide 15 by 6 15 ÷ 6 = 2 (quotient), remainder = 15 - (6×2) = 3</p>

38 <p>Divide 15 by 6 15 ÷ 6 = 2 (quotient), remainder = 15 - (6×2) = 3</p>

40 <p><strong>Step 4:</strong>Now divide the previous divisor (6) by the previous remainder (3)</p>

39 <p><strong>Step 4:</strong>Now divide the previous divisor (6) by the previous remainder (3)</p>

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

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

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

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

43 <p>The GCF of 36 and 51 is 3.</p>

42 <p>The GCF of 36 and 51 is 3.</p>

44 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 51</h2>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 51</h2>

45 <p>Finding the GCF of 36 and 51 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

44 <p>Finding the GCF of 36 and 51 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

46 <h3>Problem 1</h3>

45 <h3>Problem 1</h3>

47 <p>A library has 36 fiction books and 51 nonfiction books. They want to organize them into the largest possible groups with the same number of books in each. How many books will be in each group?</p>

46 <p>A library has 36 fiction books and 51 nonfiction books. They want to organize them into the largest possible groups with the same number of books in each. How many books will be in each group?</p>

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

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

49 <p>We should find the GCF of 36 and 51 GCF of 36 and 51 3</p>

48 <p>We should find the GCF of 36 and 51 GCF of 36 and 51 3</p>

50 <p>There are 3 equal groups 36 ÷ 3 = 12 51 ÷ 3 = 17</p>

49 <p>There are 3 equal groups 36 ÷ 3 = 12 51 ÷ 3 = 17</p>

51 <p>There will be 3 groups, and each group gets 12 fiction books and 17 nonfiction books.</p>

50 <p>There will be 3 groups, and each group gets 12 fiction books and 17 nonfiction books.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>As the GCF of 36 and 51 is 3, the library can make 3 groups.</p>

52 <p>As the GCF of 36 and 51 is 3, the library can make 3 groups.</p>

54 <p>\Now divide 36 and 51 by 3.</p>

53 <p>\Now divide 36 and 51 by 3.</p>

55 <p>Each group gets 12 fiction books and 17 nonfiction books.</p>

54 <p>Each group gets 12 fiction books and 17 nonfiction books.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>A conference has 36 chairs for panelists and 51 chairs for attendees. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

57 <p>A conference has 36 chairs for panelists and 51 chairs for attendees. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

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

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

60 <p>GCF of 36 and 51 3 So each row will have 3 chairs.</p>

59 <p>GCF of 36 and 51 3 So each row will have 3 chairs.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>There are 36 chairs for panelists and 51 chairs for attendees.</p>

61 <p>There are 36 chairs for panelists and 51 chairs for attendees.</p>

63 <p>To find the total number of chairs in each row, we should find the GCF of 36 and 51.</p>

62 <p>To find the total number of chairs in each row, we should find the GCF of 36 and 51.</p>

64 <p>There will be 3 chairs in each row.</p>

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

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

65 <h3>Problem 3</h3>

67 <p>A gardener has 36 roses and 51 tulips. She wants to plant them in rows with the same number of flowers in each row, using the longest possible row. How many flowers should be in each row?</p>

66 <p>A gardener has 36 roses and 51 tulips. She wants to plant them in rows with the same number of flowers in each row, using the longest possible row. How many flowers should be in each row?</p>

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

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

69 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 51</p>

68 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 51</p>

70 <p>The GCF of 36 and 51 3</p>

69 <p>The GCF of 36 and 51 3</p>

71 <p>The length of each row is 3 flowers.</p>

70 <p>The length of each row is 3 flowers.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>For calculating the longest row of flowers, first, we need to calculate the GCF of 36 and 51, which is 3.</p>

72 <p>For calculating the longest row of flowers, first, we need to calculate the GCF of 36 and 51, which is 3.</p>

74 <p>The length of each row of flowers will be 3.</p>

73 <p>The length of each row of flowers will be 3.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

75 <h3>Problem 4</h3>

77 <p>A carpenter has two wooden planks, one 36 cm long and the other 51 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>

76 <p>A carpenter has two wooden planks, one 36 cm long and the other 51 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>

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

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

79 <p>The carpenter needs the longest piece of wood GCF of 36 and 51 3</p>

78 <p>The carpenter needs the longest piece of wood GCF of 36 and 51 3</p>

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

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

81 <h3>Explanation</h3>

80 <h3>Explanation</h3>

82 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 51 cm, respectively, we have to find the GCF of 36 and 51, which is 3 cm.</p>

81 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 51 cm, respectively, we have to find the GCF of 36 and 51, which is 3 cm.</p>

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

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

84 <p>Well explained 👍</p>

83 <p>Well explained 👍</p>

85 <h3>Problem 5</h3>

84 <h3>Problem 5</h3>

86 <p>If the GCF of 36 and ‘b’ is 3, and the LCM is 612, find ‘b’.</p>

85 <p>If the GCF of 36 and ‘b’ is 3, and the LCM is 612, find ‘b’.</p>

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

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

88 <p>The value of ‘b’ is 51.</p>

87 <p>The value of ‘b’ is 51.</p>

89 <h3>Explanation</h3>

88 <h3>Explanation</h3>

90 <p>GCF x LCM = product of the numbers</p>

89 <p>GCF x LCM = product of the numbers</p>

91 <p>3 × 612 = 36 × b</p>

90 <p>3 × 612 = 36 × b</p>

92 <p>1836 = 36b</p>

91 <p>1836 = 36b</p>

93 <p>b = 1836 ÷ 36 = 51</p>

92 <p>b = 1836 ÷ 36 = 51</p>

94 <p>Well explained 👍</p>

93 <p>Well explained 👍</p>

95 <h2>FAQs on the Greatest Common Factor of 36 and 51</h2>

94 <h2>FAQs on the Greatest Common Factor of 36 and 51</h2>

96 <h3>1.What is the LCM of 36 and 51?</h3>

95 <h3>1.What is the LCM of 36 and 51?</h3>

97 <p>The LCM of 36 and 51 is 612.</p>

96 <p>The LCM of 36 and 51 is 612.</p>

98 <h3>2.Is 36 divisible by 3?</h3>

97 <h3>2.Is 36 divisible by 3?</h3>

99 <p>Yes, 36 is divisible by 3 because the<a>sum</a>of its digits (3+6=9) is divisible by 3.</p>

98 <p>Yes, 36 is divisible by 3 because the<a>sum</a>of its digits (3+6=9) is divisible by 3.</p>

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

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

101 <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 <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>

102 <h3>4.What is the prime factorization of 51?</h3>

101 <h3>4.What is the prime factorization of 51?</h3>

103 <p>The prime factorization of 51 is 3 x 17.</p>

102 <p>The prime factorization of 51 is 3 x 17.</p>

104 <h3>5.Are 36 and 51 prime numbers?</h3>

103 <h3>5.Are 36 and 51 prime numbers?</h3>

105 <p>No, 36 and 51 are not prime numbers because both of them have more than two factors.</p>

104 <p>No, 36 and 51 are not prime numbers because both of them have more than two factors.</p>

106 <h2>Important Glossaries for GCF of 36 and 51</h2>

105 <h2>Important Glossaries for GCF of 36 and 51</h2>

107 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.</li>

106 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.</li>

108 </ul><ul><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 </ul><ul><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>

109 </ul><ul><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 51 are 3 and 17.</li>

108 </ul><ul><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 51 are 3 and 17.</li>

110 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.</li>

109 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.</li>

111 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 51 is 612.</li>

110 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 51 is 612.</li>

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

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

113 <p>▶</p>

112 <p>▶</p>

114 <h2>Hiralee Lalitkumar Makwana</h2>

113 <h2>Hiralee Lalitkumar Makwana</h2>

115 <h3>About the Author</h3>

114 <h3>About the Author</h3>

116 <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 <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>

117 <h3>Fun Fact</h3>

116 <h3>Fun Fact</h3>

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

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