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2 <p>Last updated on<strong>August 5, 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 to schedule events. In this topic, we will learn about the GCF of 42 and 63.</p>

4 <h2>What is the GCF of 42 and 63?</h2>

5 <p>The<a>greatest common factor</a>of 42 and 63 is 21. 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. The GCF of two numbers cannot be negative because divisors are always positive.</p>

6 <h2>How to find the GCF of 42 and 63?</h2>

7 <p>To find the GCF of 42 and 63, a few methods are described below:</p>

8 <ul><li>Listing Factors</li>

9 </ul><ul><li>Prime Factorization</li>

10 </ul><ul><li>Long Division Method / by Euclidean Algorithm</li>

11 </ul><h3>GCF of 42 and 63 by Using Listing of factors</h3>

12 <p>Steps to find the GCF of 42 and 63 using the listing of<a>factors</a>:</p>

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

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

15 <p>Factors of 63 = 1, 3, 7, 9, 21, 63.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them. Common factors of 42 and 63: 1, 3, 7, 21.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor:</p>

18 <p>The largest factor that both numbers have is 21.</p>

19 <p>The GCF of 42 and 63 is 21.</p>

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22 <h3>GCF of 42 and 63 Using Prime Factorization</h3>

21 <h3>GCF of 42 and 63 Using Prime Factorization</h3>

23 <p>To find the GCF of 42 and 63 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 42 and 63 using the Prime Factorization Method, follow these steps:</p>

24 <p><strong>Step 1:</strong>Find the prime Factors of each number:</p>

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

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

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

26 <p>Prime Factors of 63: 63 = 3 x 3 x 7</p>

25 <p>Prime Factors of 63: 63 = 3 x 3 x 7</p>

27 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>. The common prime factors are: 3 x 7</p>

26 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>. The common prime factors are: 3 x 7</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 3 x 7 = 21.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 3 x 7 = 21.</p>

29 <p>The Greatest Common Factor of 42 and 63 is 21.</p>

28 <p>The Greatest Common Factor of 42 and 63 is 21.</p>

30 <h3>GCF of 42 and 63 Using Division Method or Euclidean Algorithm Method</h3>

29 <h3>GCF of 42 and 63 Using Division Method or Euclidean Algorithm Method</h3>

31 <p>Find the GCF of 42 and 63 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 42 and 63 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 63 by 42 63 ÷ 42 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 63 - (42×1) = 21</p>

32 <p>Here, divide 63 by 42 63 ÷ 42 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 63 - (42×1) = 21</p>

34 <p>The remainder is 21, not zero, so continue the process</p>

33 <p>The remainder is 21, not zero, so continue the process</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (21)</p>

34 <p><strong>Step 2:</strong>Now divide the previous divisor (42) by the previous remainder (21)</p>

36 <p>Divide 42 by 21 42 ÷ 21 = 2 (quotient), remainder = 42 - (21×2) = 0</p>

35 <p>Divide 42 by 21 42 ÷ 21 = 2 (quotient), remainder = 42 - (21×2) = 0</p>

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

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

38 <p>The GCF of 42 and 63 is 21.</p>

37 <p>The GCF of 42 and 63 is 21.</p>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 42 and 63</h2>

38 <h2>Common Mistakes and How to Avoid Them in GCF of 42 and 63</h2>

40 <p>Finding the GCF of 42 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

39 <p>Finding the GCF of 42 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

41 <h3>Problem 1</h3>

40 <h3>Problem 1</h3>

42 <p>A teacher has 42 books and 63 notebooks. 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>

41 <p>A teacher has 42 books and 63 notebooks. 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>

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

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

44 <p>We should find the GCF of 42 and 63 GCF of 42 and 63</p>

43 <p>We should find the GCF of 42 and 63 GCF of 42 and 63</p>

45 <p>3 x 7 = 21.</p>

44 <p>3 x 7 = 21.</p>

46 <p>There are 21 equal groups</p>

45 <p>There are 21 equal groups</p>

47 <p>42 ÷ 21 = 2</p>

46 <p>42 ÷ 21 = 2</p>

48 <p>63 ÷ 21 = 3</p>

47 <p>63 ÷ 21 = 3</p>

49 <p>There will be 21 groups, and each group gets 2 books and 3 notebooks.</p>

48 <p>There will be 21 groups, and each group gets 2 books and 3 notebooks.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>As the GCF of 42 and 63 is 21, the teacher can make 21 groups.</p>

50 <p>As the GCF of 42 and 63 is 21, the teacher can make 21 groups.</p>

52 <p>Now divide 42 and 63 by 21.</p>

51 <p>Now divide 42 and 63 by 21.</p>

53 <p>Each group gets 2 books and 3 notebooks.</p>

52 <p>Each group gets 2 books and 3 notebooks.</p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 2</h3>

54 <h3>Problem 2</h3>

56 <p>A school has 42 red chairs and 63 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>

55 <p>A school has 42 red chairs and 63 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>

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

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

58 <p>GCF of 42 and 63 3 x 7 = 21. So each row will have 21 chairs.</p>

57 <p>GCF of 42 and 63 3 x 7 = 21. So each row will have 21 chairs.</p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>There are 42 red and 63 blue chairs. To find the total number of chairs in each row, we should find the GCF of 42 and 63. There will be 21 chairs in each row.</p>

59 <p>There are 42 red and 63 blue chairs. To find the total number of chairs in each row, we should find the GCF of 42 and 63. There will be 21 chairs in each row.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

61 <h3>Problem 3</h3>

63 <p>A tailor has 42 meters of red fabric and 63 meters of blue 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>

62 <p>A tailor has 42 meters of red fabric and 63 meters of blue 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>

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

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

65 <p>For calculating the longest equal length, we have to calculate the GCF of 42 and 63.</p>

64 <p>For calculating the longest equal length, we have to calculate the GCF of 42 and 63.</p>

66 <p>The GCF of 42 and 63</p>

65 <p>The GCF of 42 and 63</p>

67 <p>3 x 7 = 21.</p>

66 <p>3 x 7 = 21.</p>

68 <p>The fabric is 21 meters long.</p>

67 <p>The fabric is 21 meters long.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 42 and 63, which is 21. The length of each piece of fabric will be 21 meters.</p>

69 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 42 and 63, which is 21. The length of each piece of fabric will be 21 meters.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A carpenter has two wooden planks, one 42 cm long and the other 63 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>

72 <p>A carpenter has two wooden planks, one 42 cm long and the other 63 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>

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

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

75 <p>The carpenter needs the longest piece of wood GCF of 42 and 63</p>

74 <p>The carpenter needs the longest piece of wood GCF of 42 and 63</p>

76 <p>3 x 7 = 21.</p>

75 <p>3 x 7 = 21.</p>

77 <p>The longest length of each piece is 21 cm.</p>

76 <p>The longest length of each piece is 21 cm.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>To find the longest length of each piece of the two wooden planks, 42 cm and 63 cm, respectively, we have to find the GCF of 42 and 63, which is 21 cm. The longest length of each piece is 21 cm.</p>

78 <p>To find the longest length of each piece of the two wooden planks, 42 cm and 63 cm, respectively, we have to find the GCF of 42 and 63, which is 21 cm. The longest length of each piece is 21 cm.</p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h3>Problem 5</h3>

80 <h3>Problem 5</h3>

82 <p>If the GCF of 42 and ‘a’ is 21, and the LCM is 126. Find ‘a’.</p>

81 <p>If the GCF of 42 and ‘a’ is 21, and the LCM is 126. Find ‘a’.</p>

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

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

84 <p>The value of ‘a’ is 63.</p>

83 <p>The value of ‘a’ is 63.</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

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

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

87 <p>21 × 126 = 42 × a</p>

86 <p>21 × 126 = 42 × a</p>

88 <p>2646 = 42a</p>

87 <p>2646 = 42a</p>

89 <p>a = 2646 ÷ 42 = 63</p>

88 <p>a = 2646 ÷ 42 = 63</p>

90 <p>Well explained 👍</p>

89 <p>Well explained 👍</p>

91 <h2>FAQs on the Greatest Common Factor of 42 and 63</h2>

90 <h2>FAQs on the Greatest Common Factor of 42 and 63</h2>

92 <h3>1.What is the LCM of 42 and 63?</h3>

91 <h3>1.What is the LCM of 42 and 63?</h3>

93 <p>The LCM of 42 and 63 is 126.</p>

92 <p>The LCM of 42 and 63 is 126.</p>

94 <h3>2.Is 42 divisible by 2?</h3>

93 <h3>2.Is 42 divisible by 2?</h3>

95 <p>Yes, 42 is divisible by 2 because it is an even number.</p>

94 <p>Yes, 42 is divisible by 2 because it is an even number.</p>

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

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

97 <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>

96 <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>

98 <h3>4.What is the prime factorization of 63?</h3>

97 <h3>4.What is the prime factorization of 63?</h3>

99 <p>The prime factorization of 63 is 3² x 7.</p>

98 <p>The prime factorization of 63 is 3² x 7.</p>

100 <h3>5.Are 42 and 63 prime numbers?</h3>

99 <h3>5.Are 42 and 63 prime numbers?</h3>

101 <p>No, 42 and 63 are not prime numbers because both of them have more than two factors.</p>

100 <p>No, 42 and 63 are not prime numbers because both of them have more than two factors.</p>

102 <h2>Important Glossaries for GCF of 42 and 63</h2>

101 <h2>Important Glossaries for GCF of 42 and 63</h2>

103 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.</li>

102 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.</li>

104 </ul><ul><li><strong>Prime Factorization:</strong>It involves expressing a number as the product of its prime numbers. For example, the prime factorization of 42 is 2 x 3 x 7.</li>

103 </ul><ul><li><strong>Prime Factorization:</strong>It involves expressing a number as the product of its prime numbers. For example, the prime factorization of 42 is 2 x 3 x 7.</li>

105 </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 5, the remainder is 2.</li>

104 </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 5, the remainder is 2.</li>

106 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 42 and 63 is 126.</li>

105 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 42 and 63 is 126.</li>

107 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 63 is 21, as it is their largest common factor that divides the numbers completely.</li>

106 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 63 is 21, as it is their largest common factor that divides the numbers completely.</li>

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

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

109 <p>▶</p>

108 <p>▶</p>

110 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h3>About the Author</h3>

110 <h3>About the Author</h3>

112 <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>

111 <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>

113 <h3>Fun Fact</h3>

112 <h3>Fun Fact</h3>

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

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