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2 <p>Last updated on<strong>September 24, 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 to schedule events. In this topic, we will learn about the GCF of 42 and 154.</p>

4 <h2>What is the GCF of 42 and 154?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>42 and 154 is 14. 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 are always positive.</p>

7 <h2>How to find the GCF of 42 and 154?</h2>

8 <p>To find the GCF of 42 and 154, 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><h3>GCF of 42 and 154 by Using Listing of Factors</h3>

13 <p>Steps to find the GCF of 42 and 154 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42. Factors of 154 = 1, 2, 7, 11, 14, 22, 77, 154.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 42 and 154: 1, 2, 7, 14.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 14. The GCF of 42 and 154 is 14.</p>

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19 <h3>GCF of 42 and 154 Using Prime Factorization</h3>

18 <h3>GCF of 42 and 154 Using Prime Factorization</h3>

20 <p>To find the GCF of 42 and 154 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 42 and 154 using the Prime Factorization Method, follow these steps:</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 42: 42 = 2 x 3 x 7 Prime Factors of 154: 154 = 2 x 7 x 11</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 42: 42 = 2 x 3 x 7 Prime Factors of 154: 154 = 2 x 7 x 11</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 7</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 7</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 7 = 14.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 7 = 14.</p>

24 <p>The Greatest Common Factor of 42 and 154 is 14.</p>

23 <p>The Greatest Common Factor of 42 and 154 is 14.</p>

25 <h3>GCF of 42 and 154 Using Division Method or Euclidean Algorithm Method</h3>

24 <h3>GCF of 42 and 154 Using Division Method or Euclidean Algorithm Method</h3>

26 <p>Find the GCF of 42 and 154 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

25 <p>Find the GCF of 42 and 154 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 154 by 42 154 ÷ 42 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 154 - (42×3) = 28 The remainder is 28, not zero, so continue the process</p>

26 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 154 by 42 154 ÷ 42 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 154 - (42×3) = 28 The remainder is 28, not zero, so continue the process</p>

28 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (28) Divide 42 by 28 42 ÷ 28 = 1 (quotient), remainder = 42 - (28×1) = 14</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (28) Divide 42 by 28 42 ÷ 28 = 1 (quotient), remainder = 42 - (28×1) = 14</p>

29 <p><strong>Step 3:</strong>Divide 28 by the remainder 14 28 ÷ 14 = 2 (quotient), remainder = 28 - (14×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

28 <p><strong>Step 3:</strong>Divide 28 by the remainder 14 28 ÷ 14 = 2 (quotient), remainder = 28 - (14×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

30 <p>The GCF of 42 and 154 is 14.</p>

29 <p>The GCF of 42 and 154 is 14.</p>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 42 and 154</h2>

30 <h2>Common Mistakes and How to Avoid Them in GCF of 42 and 154</h2>

32 <p>Finding GCF of 42 and 154 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

31 <p>Finding GCF of 42 and 154 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <h3>Problem 1</h3>

32 <h3>Problem 1</h3>

34 <p>A farmer has 42 apple trees and 154 orange trees. He wants to plant them in equal rows, with the largest number of trees in each row. How many trees will be in each row?</p>

33 <p>A farmer has 42 apple trees and 154 orange trees. He wants to plant them in equal rows, with the largest number of trees in each row. How many trees will be in each row?</p>

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

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

36 <p>We should find the GCF of 42 and 154 GCF of 42 and 154 2 x 7 = 14. There will be 14 equal rows 42 ÷ 14 = 3 154 ÷ 14 = 11 There will be 14 rows, and each row gets 3 apple trees and 11 orange trees.</p>

35 <p>We should find the GCF of 42 and 154 GCF of 42 and 154 2 x 7 = 14. There will be 14 equal rows 42 ÷ 14 = 3 154 ÷ 14 = 11 There will be 14 rows, and each row gets 3 apple trees and 11 orange trees.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>As the GCF of 42 and 154 is 14, the farmer can make 14 rows.</p>

37 <p>As the GCF of 42 and 154 is 14, the farmer can make 14 rows.</p>

39 <p>Now divide 42 and 154 by 14.</p>

38 <p>Now divide 42 and 154 by 14.</p>

40 <p>Each row gets 3 apple trees and 11 orange trees.</p>

39 <p>Each row gets 3 apple trees and 11 orange trees.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>A gardener has 42 rose bushes and 154 tulip bulbs. They want to arrange them in clusters with the same number of plants in each cluster, using the largest possible number of plants per cluster. How many plants will be in each cluster?</p>

42 <p>A gardener has 42 rose bushes and 154 tulip bulbs. They want to arrange them in clusters with the same number of plants in each cluster, using the largest possible number of plants per cluster. How many plants will be in each cluster?</p>

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

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

45 <p>GCF of 42 and 154 2 x 7 = 14. So each cluster will have 14 plants.</p>

44 <p>GCF of 42 and 154 2 x 7 = 14. So each cluster will have 14 plants.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>There are 42 rose bushes and 154 tulip bulbs.</p>

46 <p>There are 42 rose bushes and 154 tulip bulbs.</p>

48 <p>To find the total number of plants in each cluster, we should find the GCF of 42 and 154.</p>

47 <p>To find the total number of plants in each cluster, we should find the GCF of 42 and 154.</p>

49 <p>There will be 14 plants in each cluster.</p>

48 <p>There will be 14 plants in each cluster.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>A seamstress has 42 meters of silk and 154 meters of cotton. 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>

51 <p>A seamstress has 42 meters of silk and 154 meters of cotton. 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>

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 42 and 154 The GCF of 42 and 154 2 x 7 = 14. The fabric is 14 meters long.</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 42 and 154 The GCF of 42 and 154 2 x 7 = 14. The fabric is 14 meters long.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 42 and 154 which is 14.</p>

55 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 42 and 154 which is 14.</p>

57 <p>The length of each piece of the fabric will be 14 meters.</p>

56 <p>The length of each piece of the fabric will be 14 meters.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

58 <h3>Problem 4</h3>

60 <p>A carpenter has two wooden planks, one 42 cm long and the other 154 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>

59 <p>A carpenter has two wooden planks, one 42 cm long and the other 154 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>

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

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

62 <p>The carpenter needs the longest piece of wood GCF of 42 and 154 2 x 7 = 14. The longest length of each piece is 14 cm.</p>

61 <p>The carpenter needs the longest piece of wood GCF of 42 and 154 2 x 7 = 14. The longest length of each piece is 14 cm.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>To find the longest length of each piece of the two wooden planks, 42 cm and 154 cm, respectively.</p>

63 <p>To find the longest length of each piece of the two wooden planks, 42 cm and 154 cm, respectively.</p>

65 <p>We have to find the GCF of 42 and 154, which is 14 cm.</p>

64 <p>We have to find the GCF of 42 and 154, which is 14 cm.</p>

66 <p>The longest length of each piece is 14 cm.</p>

65 <p>The longest length of each piece is 14 cm.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

67 <h3>Problem 5</h3>

69 <p>If the GCF of 42 and ‘b’ is 14, and the LCM is 462. Find ‘b’.</p>

68 <p>If the GCF of 42 and ‘b’ is 14, and the LCM is 462. Find ‘b’.</p>

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

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

71 <p>The value of ‘b’ is 154.</p>

70 <p>The value of ‘b’ is 154.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

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

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

74 <p>14 x 462 = 42 x b</p>

73 <p>14 x 462 = 42 x b</p>

75 <p>6468 = 42b</p>

74 <p>6468 = 42b</p>

76 <p>b = 6468 ÷ 42</p>

75 <p>b = 6468 ÷ 42</p>

77 <p>= 154</p>

76 <p>= 154</p>

78 <p>Well explained 👍</p>

77 <p>Well explained 👍</p>

79 <h2>FAQs on the Greatest Common Factor of 42 and 154</h2>

78 <h2>FAQs on the Greatest Common Factor of 42 and 154</h2>

80 <h3>1.What is the LCM of 42 and 154?</h3>

79 <h3>1.What is the LCM of 42 and 154?</h3>

81 <p>The LCM of 42 and 154 is 462.</p>

80 <p>The LCM of 42 and 154 is 462.</p>

82 <h3>2.Is 42 divisible by 3?</h3>

81 <h3>2.Is 42 divisible by 3?</h3>

83 <p>Yes, 42 is divisible by 3 because the<a>sum</a>of its digits (4 + 2) is 6, which is divisible by 3.</p>

82 <p>Yes, 42 is divisible by 3 because the<a>sum</a>of its digits (4 + 2) is 6, which is divisible by 3.</p>

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

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

85 <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>

84 <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>

86 <h3>4.What is the prime factorization of 154?</h3>

85 <h3>4.What is the prime factorization of 154?</h3>

87 <p>The prime factorization of 154 is 2 x 7 x 11.</p>

86 <p>The prime factorization of 154 is 2 x 7 x 11.</p>

88 <h3>5.Are 42 and 154 prime numbers?</h3>

87 <h3>5.Are 42 and 154 prime numbers?</h3>

89 <p>No, 42 and 154 are not prime numbers because both of them have more than two factors.</p>

88 <p>No, 42 and 154 are not prime numbers because both of them have more than two factors.</p>

90 <h2>Important Glossaries for GCF of 42 and 154</h2>

89 <h2>Important Glossaries for GCF of 42 and 154</h2>

91 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.</li>

90 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.</li>

92 </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>

91 </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>

93 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2.</li>

94 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 154 is 462.</li>

93 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 154 is 462.</li>

95 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 154 is 14, as it is their largest common factor that divides the numbers completely.</li>

94 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 154 is 14, as it is their largest common factor that divides the numbers completely.</li>

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

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

97 <p>▶</p>

96 <p>▶</p>

98 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h2>Hiralee Lalitkumar Makwana</h2>

99 <h3>About the Author</h3>

98 <h3>About the Author</h3>

100 <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>

99 <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>

101 <h3>Fun Fact</h3>

100 <h3>Fun Fact</h3>

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

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