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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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 36 and 63.</p>

4 <h2>What is the GCF of 36 and 63?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>36 and 63 is 9. 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 36 and 63?</h2>

7 <p>To find the GCF of 36 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 36 and 63 by Using Listing of Factors</h3>

12 <p>Steps to find the GCF of 36 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 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</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 36 and 63: 1, 3, 9.</p>

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

18 <p>The largest factor that both numbers have is 9.</p>

19 <p>The GCF of 36 and 63 is 9.</p>

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22 <h3>GCF of 36 and 63 Using Prime Factorization</h3>

21 <h3>GCF of 36 and 63 Using Prime Factorization</h3>

23 <p>To find the GCF of 36 and 63 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 36 and 63 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 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>

24 <p>Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>

26 <p>Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7</p>

25 <p>Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors.</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors.</p>

28 <p>The common prime factors are: 3 x 3 = 3²</p>

27 <p>The common prime factors are: 3 x 3 = 3²</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors 3² = 9.</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 3² = 9.</p>

30 <p>The Greatest Common Factor of 36 and 63 is 9.</p>

29 <p>The Greatest Common Factor of 36 and 63 is 9.</p>

31 <h3>GCF of 36 and 63 Using Division Method or Euclidean Algorithm Method</h3>

30 <h3>GCF of 36 and 63 Using Division Method or Euclidean Algorithm Method</h3>

32 <p>Find the GCF of 36 and 63 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 36 and 63 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

34 <p>Here, divide 63 by 36 63 ÷ 36 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 63 - (36×1) = 27</p>

33 <p>Here, divide 63 by 36 63 ÷ 36 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 63 - (36×1) = 27</p>

35 <p>The remainder is 27, not zero, so continue the process</p>

34 <p>The remainder is 27, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (27)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (27)</p>

37 <p>Divide 36 by 27 36 ÷ 27 = 1 (quotient), remainder = 36 - (27×1) = 9</p>

36 <p>Divide 36 by 27 36 ÷ 27 = 1 (quotient), remainder = 36 - (27×1) = 9</p>

38 <p><strong>Step 3:</strong>Now divide the previous divisor (27) by the previous remainder (9)</p>

37 <p><strong>Step 3:</strong>Now divide the previous divisor (27) by the previous remainder (9)</p>

39 <p>Divide 27 by 9 27 ÷ 9 = 3 (quotient), remainder = 27 - (9×3) = 0</p>

38 <p>Divide 27 by 9 27 ÷ 9 = 3 (quotient), remainder = 27 - (9×3) = 0</p>

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

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

41 <p>The GCF of 36 and 63 is 9.</p>

40 <p>The GCF of 36 and 63 is 9.</p>

42 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 63</h2>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 63</h2>

43 <p>Finding the GCF of 36 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

42 <p>Finding the GCF of 36 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

44 <h3>Problem 1</h3>

43 <h3>Problem 1</h3>

45 <p>A teacher has 36 apples and 63 oranges. She wants to pack them into equal boxes with the largest number of fruits in each box. How many fruits will be in each box?</p>

44 <p>A teacher has 36 apples and 63 oranges. She wants to pack them into equal boxes with the largest number of fruits in each box. How many fruits will be in each box?</p>

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

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

47 <p>We should find the GCF of 36 and 63.</p>

46 <p>We should find the GCF of 36 and 63.</p>

48 <p>GCF of 36 and 63</p>

47 <p>GCF of 36 and 63</p>

49 <p>3² = 9.</p>

48 <p>3² = 9.</p>

50 <p>There are 9 equal boxes</p>

49 <p>There are 9 equal boxes</p>

51 <p>36 ÷ 9 = 4</p>

50 <p>36 ÷ 9 = 4</p>

52 <p>63 ÷ 9 = 7</p>

51 <p>63 ÷ 9 = 7</p>

53 <p>There will be 9 boxes, and each box gets 4 apples and 7 oranges.</p>

52 <p>There will be 9 boxes, and each box gets 4 apples and 7 oranges.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>As the GCF of 36 and 63 is 9, the teacher can make 9 boxes.</p>

54 <p>As the GCF of 36 and 63 is 9, the teacher can make 9 boxes.</p>

56 <p>Now divide 36 and 63 by 9.</p>

55 <p>Now divide 36 and 63 by 9.</p>

57 <p>Each box gets 4 apples and 7 oranges.</p>

56 <p>Each box gets 4 apples and 7 oranges.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 2</h3>

58 <h3>Problem 2</h3>

60 <p>A school has 36 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>

59 <p>A school has 36 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>

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

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

62 <p>GCF of 36 and 63</p>

61 <p>GCF of 36 and 63</p>

63 <p>3² = 9.</p>

62 <p>3² = 9.</p>

64 <p>So each row will have 9 chairs.</p>

63 <p>So each row will have 9 chairs.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>There are 36 red and 63 blue chairs.</p>

65 <p>There are 36 red and 63 blue chairs.</p>

67 <p>To find the total number of chairs in each row, we should find the GCF of 36 and 63.</p>

66 <p>To find the total number of chairs in each row, we should find the GCF of 36 and 63.</p>

68 <p>There will be 9 chairs in each row.</p>

67 <p>There will be 9 chairs in each row.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h3>Problem 3</h3>

69 <h3>Problem 3</h3>

71 <p>A tailor has 36 meters of silk ribbon and 63 meters of cotton 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>

70 <p>A tailor has 36 meters of silk ribbon and 63 meters of cotton 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>

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

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

73 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 63</p>

72 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 63</p>

74 <p>The GCF of 36 and 63</p>

73 <p>The GCF of 36 and 63</p>

75 <p>3² = 9.</p>

74 <p>3² = 9.</p>

76 <p>The ribbon is 9 meters long.</p>

75 <p>The ribbon is 9 meters long.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 36 and 63, which is 9. The length of each piece of the ribbon will be 9 meters.</p>

77 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 36 and 63, which is 9. The length of each piece of the ribbon will be 9 meters.</p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h3>Problem 4</h3>

79 <h3>Problem 4</h3>

81 <p>A carpenter has two wooden planks, one 36 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>

80 <p>A carpenter has two wooden planks, one 36 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>

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

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

83 <p>The carpenter needs the longest piece of wood GCF of 36 and 63 3² = 9.</p>

82 <p>The carpenter needs the longest piece of wood GCF of 36 and 63 3² = 9.</p>

84 <p>The longest length of each piece is 9 cm.</p>

83 <p>The longest length of each piece is 9 cm.</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

86 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 63 cm, respectively. We have to find the GCF of 36 and 63, which is 9 cm. The longest length of each piece is 9 cm.</p>

85 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 63 cm, respectively. We have to find the GCF of 36 and 63, which is 9 cm. The longest length of each piece is 9 cm.</p>

87 <p>Well explained 👍</p>

86 <p>Well explained 👍</p>

88 <h3>Problem 5</h3>

87 <h3>Problem 5</h3>

89 <p>If the GCF of 36 and ‘b’ is 9, and the LCM is 252. Find ‘b’.</p>

88 <p>If the GCF of 36 and ‘b’ is 9, and the LCM is 252. Find ‘b’.</p>

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

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

91 <p>The value of ‘b’ is 63.</p>

90 <p>The value of ‘b’ is 63.</p>

92 <h3>Explanation</h3>

91 <h3>Explanation</h3>

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

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

94 <p>9 × 252 = 36 × b</p>

93 <p>9 × 252 = 36 × b</p>

95 <p>2268 = 36b</p>

94 <p>2268 = 36b</p>

96 <p>b = 2268 ÷ 36 = 63</p>

95 <p>b = 2268 ÷ 36 = 63</p>

97 <p>Well explained 👍</p>

96 <p>Well explained 👍</p>

98 <h2>FAQs on the Greatest Common Factor of 36 and 63</h2>

97 <h2>FAQs on the Greatest Common Factor of 36 and 63</h2>

99 <h3>1.What is the LCM of 36 and 63?</h3>

98 <h3>1.What is the LCM of 36 and 63?</h3>

100 <p>The LCM of 36 and 63 is 252.</p>

99 <p>The LCM of 36 and 63 is 252.</p>

101 <h3>2.Is 36 divisible by 3?</h3>

100 <h3>2.Is 36 divisible by 3?</h3>

102 <p>Yes, 36 is divisible by 3 because the<a>sum</a>of its digits (3+6) is 9, which is divisible by 3.</p>

101 <p>Yes, 36 is divisible by 3 because the<a>sum</a>of its digits (3+6) is 9, which is divisible by 3.</p>

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

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

104 <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>

103 <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>

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

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

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

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

107 <h3>5.Are 36 and 63 prime numbers?</h3>

106 <h3>5.Are 36 and 63 prime numbers?</h3>

108 <p>No, 36 and 63 are not prime numbers because both of them have more than two factors.</p>

107 <p>No, 36 and 63 are not prime numbers because both of them have more than two factors.</p>

109 <h2>Important Glossaries for GCF of 36 and 63</h2>

108 <h2>Important Glossaries for GCF of 36 and 63</h2>

110 <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>

109 <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>

111 </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 18 are 2 and 3.</li>

110 </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 18 are 2 and 3.</li>

112 </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.</li>

111 </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.</li>

113 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 9 is 18.</li>

112 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 9 is 18.</li>

114 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 63 is 9, as it is their largest common factor that divides the numbers completely.</li>

113 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 63 is 9, as it is their largest common factor that divides the numbers completely.</li>

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

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

116 <p>▶</p>

115 <p>▶</p>

117 <h2>Hiralee Lalitkumar Makwana</h2>

116 <h2>Hiralee Lalitkumar Makwana</h2>

118 <h3>About the Author</h3>

117 <h3>About the Author</h3>

119 <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>

118 <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>

120 <h3>Fun Fact</h3>

119 <h3>Fun Fact</h3>

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

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