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2 <p>Last updated on<strong>August 11, 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 54 and 42.</p>

4 <h2>What is the GCF of 54 and 42?</h2>

5 <p>The<a>greatest common factor</a>of 54 and 42 is 6. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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 54 and 42?</h2>

8 <p>To find the GCF of 54 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 54 and 42 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 54 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 54 = 1, 2, 3, 6, 9, 18, 27, 54.</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 54 and 42: 1, 2, 3, 6.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 6. The GCF of 54 and 42 is 6.</p>

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21 <h2>GCF of 54 and 42 Using Prime Factorization</h2>

20 <h2>GCF of 54 and 42 Using Prime Factorization</h2>

22 <p>To find the GCF of 54 and 42 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 54 and 42 using the Prime Factorization Method, follow these steps:</p>

23 <p><strong>Step 1:</strong>Find the prime Factors of each number Prime Factors of 54: 54 = 2 x 3 x 3 x 3 = 2 x 33</p>

22 <p><strong>Step 1:</strong>Find the prime Factors of each number Prime Factors of 54: 54 = 2 x 3 x 3 x 3 = 2 x 33</p>

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

23 <p>Prime Factors of 42: 42 = 2 x 3 x 7</p>

25 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>The common prime factors are: 2 x 3 = 6</p>

24 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>The common prime factors are: 2 x 3 = 6</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 54 and 42 is 6.</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 54 and 42 is 6.</p>

27 <h2>GCF of 54 and 42 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 54 and 42 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 54 and 42 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 54 and 42 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

30 <p>Here, divide 54 by 42 54 ÷ 42 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 54 - (42×1) = 12.</p>

29 <p>Here, divide 54 by 42 54 ÷ 42 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 54 - (42×1) = 12.</p>

31 <p>The remainder is 12, not zero, so continue the process</p>

30 <p>The remainder is 12, not zero, so continue the process</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (12) Divide 42 by 12 42 ÷ 12 = 3 (quotient), remainder = 42 - (12×3) = 6.</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (12) Divide 42 by 12 42 ÷ 12 = 3 (quotient), remainder = 42 - (12×3) = 6.</p>

33 <p><strong>Step 3:</strong>Now, divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 - (6×2) = 0</p>

32 <p><strong>Step 3:</strong>Now, divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 - (6×2) = 0</p>

34 <p>The remainder is zero, the divisor will become the GCF. The GCF of 54 and 42 is 6.</p>

33 <p>The remainder is zero, the divisor will become the GCF. The GCF of 54 and 42 is 6.</p>

35 <h2>Common Mistakes and How to Avoid Them in GCF of 54 and 42</h2>

34 <h2>Common Mistakes and How to Avoid Them in GCF of 54 and 42</h2>

36 <p>Finding the GCF of 54 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 <p>Finding the GCF of 54 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>

37 <h3>Problem 1</h3>

36 <h3>Problem 1</h3>

38 <p>A farmer has 54 apples and 42 oranges. He wants to pack them into boxes with the largest number of each fruit in every box. How many pieces of fruit will each box contain?</p>

37 <p>A farmer has 54 apples and 42 oranges. He wants to pack them into boxes with the largest number of each fruit in every box. How many pieces of fruit will each box contain?</p>

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

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

40 <p>We should find the GCF of 54 and 42 GCF of 54 and 42 is 6. There are 6 equal groups. 54 ÷ 6 = 9 42 ÷ 6 = 7 There will be 6 boxes, and each box gets 9 apples and 7 oranges.</p>

39 <p>We should find the GCF of 54 and 42 GCF of 54 and 42 is 6. There are 6 equal groups. 54 ÷ 6 = 9 42 ÷ 6 = 7 There will be 6 boxes, and each box gets 9 apples and 7 oranges.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 54 and 42 is 6, the farmer can make 6 boxes. Now divide 54 and 42 by 6. Each box gets 9 apples and 7 oranges.</p>

41 <p>As the GCF of 54 and 42 is 6, the farmer can make 6 boxes. Now divide 54 and 42 by 6. Each box gets 9 apples and 7 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 concert hall has 54 chairs in one section and 42 chairs in another section. 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 concert hall has 54 chairs in one section and 42 chairs in another section. 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 54 and 42 is 6. So each row will have 6 chairs.</p>

46 <p>GCF of 54 and 42 is 6. So each row will have 6 chairs.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 54 chairs in one section and 42 chairs in another section. To find the total number of chairs in each row, we should find the GCF of 54 and 42. There will be 6 chairs in each row.</p>

48 <p>There are 54 chairs in one section and 42 chairs in another section. To find the total number of chairs in each row, we should find the GCF of 54 and 42. There will be 6 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 ribbon supplier has 54 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 ribbon supplier has 54 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 54 and 42. The GCF of 54 and 42 is 6. The ribbon pieces are 6 meters long.</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 54 and 42. The GCF of 54 and 42 is 6. The ribbon pieces are 6 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 54 and 42, which is 6. The length of each piece of the ribbon will be 6 meters.</p>

55 <p>For calculating the longest length of the ribbon first, we need to calculate the GCF of 54 and 42, which is 6. The length of each piece of the ribbon will be 6 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 54 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 54 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 54 and 42 is 6. The longest length of each piece is 6 cm.</p>

60 <p>The carpenter needs the longest piece of wood GCF of 54 and 42 is 6. The longest length of each piece is 6 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, 54 cm and 42 cm, respectively, we have to find the GCF of 54 and 42, which is 6 cm. The longest length of each piece is 6 cm.</p>

62 <p>To find the longest length of each piece of the two wooden planks, 54 cm and 42 cm, respectively, we have to find the GCF of 54 and 42, which is 6 cm. The longest length of each piece is 6 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 54 and ‘a’ is 6, and the LCM is 378. Find ‘a’.</p>

65 <p>If the GCF of 54 and ‘a’ is 6, and the LCM is 378. 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 6 × 378 = 54 × a 2268 = 54a a = 2268 ÷ 54 = 42</p>

69 <p>GCF x LCM = product of the numbers 6 × 378 = 54 × a 2268 = 54a a = 2268 ÷ 54 = 42</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQs on the Greatest Common Factor of 54 and 42</h2>

71 <h2>FAQs on the Greatest Common Factor of 54 and 42</h2>

73 <h3>1.What is the LCM of 54 and 42?</h3>

72 <h3>1.What is the LCM of 54 and 42?</h3>

74 <p>The LCM of 54 and 42 is 378.</p>

73 <p>The LCM of 54 and 42 is 378.</p>

75 <h3>2.Is 54 divisible by 3?</h3>

74 <h3>2.Is 54 divisible by 3?</h3>

76 <p>Yes, 54 is divisible by 3 because the<a>sum</a>of its digits (5 + 4) is 9, which is divisible by 3.</p>

75 <p>Yes, 54 is divisible by 3 because the<a>sum</a>of its digits (5 + 4) is 9, which is divisible by 3.</p>

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

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

78 <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>

77 <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>

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

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

80 <p>The prime factorization of 42 is 2 x 3 x 7.</p>

79 <p>The prime factorization of 42 is 2 x 3 x 7.</p>

81 <h3>5.Are 54 and 42 prime numbers?</h3>

80 <h3>5.Are 54 and 42 prime numbers?</h3>

82 <p>No, 54 and 42 are not prime numbers because both of them have more than two factors.</p>

81 <p>No, 54 and 42 are not prime numbers because both of them have more than two factors.</p>

83 <h2>Important Glossaries for GCF of 54 and 42</h2>

82 <h2>Important Glossaries for GCF of 54 and 42</h2>

84 <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>

83 <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>

85 </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>

84 </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>

86 </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 21 are 3 and 7.</li>

85 </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 21 are 3 and 7.</li>

87 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

86 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

88 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 54 and 42 is 378.</li>

87 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 54 and 42 is 378.</li>

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

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

90 <p>▶</p>

89 <p>▶</p>

91 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h2>Hiralee Lalitkumar Makwana</h2>

92 <h3>About the Author</h3>

91 <h3>About the Author</h3>

93 <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>

92 <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>

94 <h3>Fun Fact</h3>

93 <h3>Fun Fact</h3>

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

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