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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 72 and 39.</p>

4 <h2>What is the GCF of 72 and 39?</h2>

5 <p>The<a>greatest common factor</a>of 72 and 39 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 72 and 39?</h2>

8 <p>To find the GCF of 72 and 39, 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 72 and 39 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 72 and 39 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 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.</p>

16 <p>Factors of 39 = 1, 3, 13, 39.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 72 and 39: 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 72 and 39 is 3.</p>

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22 <h2>GCF of 72 and 39 Using Prime Factorization</h2>

21 <h2>GCF of 72 and 39 Using Prime Factorization</h2>

23 <p>To find the GCF of 72 and 39 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 72 and 39 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 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²</p>

24 <p>Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²</p>

26 <p>Prime Factors of 39: 39 = 3 × 13</p>

25 <p>Prime Factors of 39: 39 = 3 × 13</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 factors 3 = 3</p>

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

29 <p>The Greatest Common Factor of 72 and 39 is 3.</p>

28 <p>The Greatest Common Factor of 72 and 39 is 3.</p>

30 <h2>GCF of 72 and 39 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 72 and 39 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 72 and 39 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 72 and 39 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 72 by 39 72 ÷ 39 = 1 (<a>quotient</a>),</p>

32 <p>Here, divide 72 by 39 72 ÷ 39 = 1 (<a>quotient</a>),</p>

34 <p>The<a>remainder</a>is calculated as 72 - (39×1) = 33</p>

33 <p>The<a>remainder</a>is calculated as 72 - (39×1) = 33</p>

35 <p>The remainder is 33, not zero, so continue the process</p>

34 <p>The remainder is 33, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (39) by the previous remainder (33)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (39) by the previous remainder (33)</p>

37 <p>Divide 39 by 33 39 ÷ 33 = 1 (quotient), remainder = 39 - (33×1) = 6</p>

36 <p>Divide 39 by 33 39 ÷ 33 = 1 (quotient), remainder = 39 - (33×1) = 6</p>

38 <p><strong>Step 3:</strong>Now divide the previous divisor (33) by the previous remainder (6)</p>

37 <p><strong>Step 3:</strong>Now divide the previous divisor (33) by the previous remainder (6)</p>

39 <p>Divide 33 by 6 33 ÷ 6 = 5 (quotient), remainder = 33 - (6×5) = 3</p>

38 <p>Divide 33 by 6 33 ÷ 6 = 5 (quotient), remainder = 33 - (6×5) = 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 72 and 39 is 3.</p>

42 <p>The GCF of 72 and 39 is 3.</p>

44 <h2>Common Mistakes and How to Avoid Them in GCF of 72 and 39</h2>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 72 and 39</h2>

45 <p>Finding the GCF of 72 and 39 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 72 and 39 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 baker has 72 cookies and 39 cupcakes. She wants to pack them into boxes with the same number of items in each box, using the largest number of items possible. How many items will be in each box?</p>

46 <p>A baker has 72 cookies and 39 cupcakes. She wants to pack them into boxes with the same number of items in each box, using the largest number of items possible. How many items will be in each box?</p>

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

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

49 <p>We should find the GCF of 72 and 39 GCF of 72 and 39 3</p>

48 <p>We should find the GCF of 72 and 39 GCF of 72 and 39 3</p>

50 <p>There are 3 equal items per box. 72 ÷ 3 = 24 39 ÷ 3 = 13</p>

49 <p>There are 3 equal items per box. 72 ÷ 3 = 24 39 ÷ 3 = 13</p>

51 <p>There will be 3 items in each box, with 24 boxes containing cookies and 13 boxes containing cupcakes.</p>

50 <p>There will be 3 items in each box, with 24 boxes containing cookies and 13 boxes containing cupcakes.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>As the GCF of 72 and 39 is 3, the baker can make boxes containing 3 items each.</p>

52 <p>As the GCF of 72 and 39 is 3, the baker can make boxes containing 3 items each.</p>

54 <p>Now divide 72 and 39 by 3.</p>

53 <p>Now divide 72 and 39 by 3.</p>

55 <p>Each box contains 3 items.</p>

54 <p>Each box contains 3 items.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>A gardener has 72 tulip bulbs and 39 daffodil bulbs. They want to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?</p>

57 <p>A gardener has 72 tulip bulbs and 39 daffodil bulbs. They want to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?</p>

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

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

60 <p>GCF of 72 and 39 3 So each row will have 3 bulbs.</p>

59 <p>GCF of 72 and 39 3 So each row will have 3 bulbs.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>There are 72 tulip bulbs and 39 daffodil bulbs.</p>

61 <p>There are 72 tulip bulbs and 39 daffodil bulbs.</p>

63 <p>To find the total number of bulbs in each row, we should find the GCF of 72 and 39.</p>

62 <p>To find the total number of bulbs in each row, we should find the GCF of 72 and 39.</p>

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

63 <p>There will be 3 bulbs 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 tailor has 72 meters of silk and 39 meters of cotton 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>

66 <p>A tailor has 72 meters of silk and 39 meters of cotton 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>

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 72 and 39</p>

68 <p>For calculating the longest equal length, we have to calculate the GCF of 72 and 39</p>

70 <p>The GCF of 72 and 39 3</p>

69 <p>The GCF of 72 and 39 3</p>

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

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

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>For calculating the longest length of fabric, first we need to calculate the GCF of 72 and 39, which is 3.</p>

72 <p>For calculating the longest length of fabric, first we need to calculate the GCF of 72 and 39, which is 3.</p>

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

73 <p>The length of each piece of fabric will be 3 meters.</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 boards, one 72 cm long and the other 39 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 boards, one 72 cm long and the other 39 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 72 and 39 3</p>

78 <p>The carpenter needs the longest piece of wood GCF of 72 and 39 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 boards, 72 cm and 39 cm, respectively, we have to find the GCF of 72 and 39, which is 3 cm.</p>

81 <p>To find the longest length of each piece of the two wooden boards, 72 cm and 39 cm, respectively, we have to find the GCF of 72 and 39, 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 72 and ‘b’ is 3, and the LCM is 936. Find ‘b’.</p>

85 <p>If the GCF of 72 and ‘b’ is 3, and the LCM is 936. Find ‘b’.</p>

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

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

88 <p>The value of ‘b’ is 39.</p>

87 <p>The value of ‘b’ is 39.</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 × 936 = 72 × b</p>

90 <p>3 × 936 = 72 × b</p>

92 <p>2808 = 72b</p>

91 <p>2808 = 72b</p>

93 <p>b = 2808 ÷ 72 = 39</p>

92 <p>b = 2808 ÷ 72 = 39</p>

94 <p>Well explained 👍</p>

93 <p>Well explained 👍</p>

95 <h2>FAQs on the Greatest Common Factor of 72 and 39</h2>

94 <h2>FAQs on the Greatest Common Factor of 72 and 39</h2>

96 <h3>1.What is the LCM of 72 and 39?</h3>

95 <h3>1.What is the LCM of 72 and 39?</h3>

97 <p>The LCM of 72 and 39 is 936.</p>

96 <p>The LCM of 72 and 39 is 936.</p>

98 <h3>2.Is 72 divisible by 4?</h3>

97 <h3>2.Is 72 divisible by 4?</h3>

99 <p>Yes, 72 is divisible by 4 because 72 ÷ 4 = 18.</p>

98 <p>Yes, 72 is divisible by 4 because 72 ÷ 4 = 18.</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 39?</h3>

101 <h3>4.What is the prime factorization of 39?</h3>

103 <p>The prime factorization of 39 is 3 × 13.</p>

102 <p>The prime factorization of 39 is 3 × 13.</p>

104 <h3>5.Are 72 and 39 prime numbers?</h3>

103 <h3>5.Are 72 and 39 prime numbers?</h3>

105 <p>No, 72 and 39 are not prime numbers because both of them have more than two factors.</p>

104 <p>No, 72 and 39 are not prime numbers because both of them have more than two factors.</p>

106 <h2>Important Glossaries for GCF of 72 and 39</h2>

105 <h2>Important Glossaries for GCF of 72 and 39</h2>

107 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>

106 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</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 4 are 4, 8, 12, 16, 20, 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 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.</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 15 are 3 and 5.</li>

110 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

109 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</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 24 and 36 is 72.</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 24 and 36 is 72.</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>