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2 <p>Last updated on<strong>August 14, 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 39 and 42.</p>

4 <h2>What is the GCF of 39 and 42?</h2>

5 <p>The<a>greatest common factor</a>of 39 and 42 is 3. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>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, which is always positive.</p>

7 <h2>How to find the GCF of 39 and 42?</h2>

8 <p>To find the GCF of 39 and 42, a few methods are described below -</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

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

12 </ol><h2>GCF of 39 and 42 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 39 and 42 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 39 = 1, 3, 13, 39.</p>

16 <p>Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 39 and 42: 1, 3.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 3. The GCF of 39 and 42 is 3.</p>

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21 <h2>GCF of 39 and 42 Using Prime Factorization</h2>

20 <h2>GCF of 39 and 42 Using Prime Factorization</h2>

22 <p>To find the GCF of 39 and 42 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 39 and 42 using the Prime Factorization Method, follow these steps:</p>

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

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

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

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

25 <p>Prime Factors of 42: 42 = 2 × 3 × 7</p>

24 <p>Prime Factors of 42: 42 = 2 × 3 × 7</p>

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

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

27 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3 The Greatest Common Factor of 39 and 42 is 3.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3 The Greatest Common Factor of 39 and 42 is 3.</p>

28 <h2>GCF of 39 and 42 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 39 and 42 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 39 and 42 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 39 and 42 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 42 by 39 42 ÷ 39 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 42 - (39×1) = 3 The remainder is 3, not zero, so continue the process</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 42 by 39 42 ÷ 39 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 42 - (39×1) = 3 The remainder is 3, not zero, so continue the process</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (39) by the previous remainder (3) Divide 39 by 3 39 ÷ 3 = 13 (quotient), remainder = 39 - (3×13) = 0</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (39) by the previous remainder (3) Divide 39 by 3 39 ÷ 3 = 13 (quotient), remainder = 39 - (3×13) = 0</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 39 and 42 is 3.</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 39 and 42 is 3.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 39 and 42</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 39 and 42</h2>

34 <p>Finding GCF of 39 and 42 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <p>Finding GCF of 39 and 42 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A teacher has 39 apples and 42 oranges. 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>

35 <p>A teacher has 39 apples and 42 oranges. 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>

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

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

38 <p>We should find the GCF of 39 and 42 GCF of 39 and 42 3</p>

37 <p>We should find the GCF of 39 and 42 GCF of 39 and 42 3</p>

39 <p>There are 3 equal groups 39 ÷ 3 = 13 42 ÷ 3 = 14</p>

38 <p>There are 3 equal groups 39 ÷ 3 = 13 42 ÷ 3 = 14</p>

40 <p>There will be 3 groups, and each group gets 13 apples and 14 oranges.</p>

39 <p>There will be 3 groups, and each group gets 13 apples and 14 oranges.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 39 and 42 is 3, the teacher can make 3 groups. Now divide 39 and 42 by 3. Each group gets 13 apples and 14 oranges.</p>

41 <p>As the GCF of 39 and 42 is 3, the teacher can make 3 groups. Now divide 39 and 42 by 3. Each group gets 13 apples and 14 oranges.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A school has 39 red chairs and 42 blue chairs. 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>

44 <p>A school has 39 red chairs and 42 blue chairs. 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>

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

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

47 <p>GCF of 39 and 42 3 So each row will have 3 chairs.</p>

46 <p>GCF of 39 and 42 3 So each row will have 3 chairs.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 39 red and 42 blue chairs. To find the total number of chairs in each row, we should find the GCF of 39 and 42. There will be 3 chairs in each row.</p>

48 <p>There are 39 red and 42 blue chairs. To find the total number of chairs in each row, we should find the GCF of 39 and 42. There will be 3 chairs in each row.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>A tailor has 39 meters of red ribbon and 42 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

51 <p>A tailor has 39 meters of red ribbon and 42 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

54 <p>For calculating the longest equal length, we have to calculate the GCF of 39 and 42 The GCF of 39 and 42 3 The ribbon is 3 meters long.</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 39 and 42 The GCF of 39 and 42 3 The ribbon is 3 meters long.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 39 and 42, which is 3. The length of each piece of the ribbon will be 3 meters.</p>

55 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 39 and 42, which is 3. The length of each piece of the ribbon will be 3 meters.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

57 <h3>Problem 4</h3>

59 <p>A carpenter has two wooden planks, one 39 cm long and the other 42 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>

58 <p>A carpenter has two wooden planks, one 39 cm long and the other 42 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>

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

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

61 <p>The carpenter needs the longest piece of wood GCF of 39 and 42 3 The longest length of each piece is 3 cm.</p>

60 <p>The carpenter needs the longest piece of wood GCF of 39 and 42 3 The longest length of each piece is 3 cm.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>To find the longest length of each piece of the two wooden planks, 39 cm and 42 cm, respectively. We have to find the GCF of 39 and 42, which is 3 cm. The longest length of each piece is 3 cm.</p>

62 <p>To find the longest length of each piece of the two wooden planks, 39 cm and 42 cm, respectively. We have to find the GCF of 39 and 42, which is 3 cm. The longest length of each piece is 3 cm.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

64 <h3>Problem 5</h3>

66 <p>If the GCF of 39 and ‘a’ is 3, and the LCM is 546. Find ‘a’.</p>

65 <p>If the GCF of 39 and ‘a’ is 3, and the LCM is 546. Find ‘a’.</p>

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

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

68 <p>The value of ‘a’ is 42.</p>

67 <p>The value of ‘a’ is 42.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

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

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

71 <p>3 × 546 = 39 × a</p>

70 <p>3 × 546 = 39 × a</p>

72 <p>1638 = 39a</p>

71 <p>1638 = 39a</p>

73 <p>a = 1638 ÷ 39 = 42</p>

72 <p>a = 1638 ÷ 39 = 42</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQs on the Greatest Common Factor of 39 and 42</h2>

74 <h2>FAQs on the Greatest Common Factor of 39 and 42</h2>

76 <h3>1.What is the LCM of 39 and 42?</h3>

75 <h3>1.What is the LCM of 39 and 42?</h3>

77 <p>The LCM of 39 and 42 is 546.</p>

76 <p>The LCM of 39 and 42 is 546.</p>

78 <h3>2.Is 39 divisible by 2?</h3>

77 <h3>2.Is 39 divisible by 2?</h3>

79 <p>No, 39 is not divisible by 2 because it is an odd number.</p>

78 <p>No, 39 is not divisible by 2 because it is an odd number.</p>

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

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

81 <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>

80 <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>

82 <h3>4.What is the prime factorization of 42?</h3>

81 <h3>4.What is the prime factorization of 42?</h3>

83 <p>The prime factorization of 42 is 2 × 3 × 7.</p>

82 <p>The prime factorization of 42 is 2 × 3 × 7.</p>

84 <h3>5.Are 39 and 42 prime numbers?</h3>

83 <h3>5.Are 39 and 42 prime numbers?</h3>

85 <p>No, 39 and 42 are not prime numbers because both of them have more than two factors.</p>

84 <p>No, 39 and 42 are not prime numbers because both of them have more than two factors.</p>

86 <h2>Important Glossaries for GCF of 39 and 42</h2>

85 <h2>Important Glossaries for GCF of 39 and 42</h2>

87 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 39 are 1, 3, 13, and 39.</li>

86 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 39 are 1, 3, 13, and 39.</li>

88 </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, and so on.</li>

87 </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, and so on.</li>

89 </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 42 are 2, 3, and 7.</li>

88 </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 42 are 2, 3, and 7.</li>

90 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 42 is divided by 39, the remainder is 3.</li>

89 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 42 is divided by 39, the remainder is 3.</li>

91 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 39 and 42 is 546.</li>

90 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 39 and 42 is 546.</li>

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Hiralee Lalitkumar Makwana</h2>

93 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h3>About the Author</h3>

94 <h3>About the Author</h3>

96 <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>

95 <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>

97 <h3>Fun Fact</h3>

96 <h3>Fun Fact</h3>

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

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