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1 - <p>165 Learners</p>

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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 9 and 12.</p>

4 <h2>What is the GCF of 9 and 12?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>9 and 12 is 3. 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 9 and 12?</h2>

7 <p>To find the GCF of 9 and 12, a few methods are described below</p>

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

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

10 </ul><h2>GCF of 9 and 12 by Using Listing of factors</h2>

11 <p>Steps to find the GCF of 9 and 12 using the listing of<a>factors</a>:</p>

12 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 9 = 1, 3, 9. Factors of 12 = 1, 2, 3, 4, 6, 12.</p>

13 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 9 and 12: 1, 3.</p>

14 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 3.</p>

15 <p>The GCF of 9 and 12 is 3.</p>

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18 <h2>GCF of 9 and 12 Using Prime Factorization</h2>

17 <h2>GCF of 9 and 12 Using Prime Factorization</h2>

19 <p>To find the GCF of 9 and 12 using the Prime Factorization Method, follow these steps:</p>

18 <p>To find the GCF of 9 and 12 using the Prime Factorization Method, follow these steps:</p>

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

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

21 <p>Prime Factors of 9: 9 = 3 x 3 = 3²</p>

20 <p>Prime Factors of 9: 9 = 3 x 3 = 3²</p>

22 <p>Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3</p>

21 <p>Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3</p>

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

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

24 <p>The common prime factor is: 3</p>

23 <p>The common prime factor is: 3</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3</p>

26 <p>The Greatest Common Factor of 9 and 12 is 3.</p>

25 <p>The Greatest Common Factor of 9 and 12 is 3.</p>

27 <h2>GCF of 9 and 12 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 9 and 12 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 9 and 12 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 9 and 12 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 12 by 9 12 ÷ 9 = 1 (<a>quotient</a>),</p>

29 <p>Here, divide 12 by 9 12 ÷ 9 = 1 (<a>quotient</a>),</p>

31 <p>The<a>remainder</a>is calculated as 12 - (9×1) = 3</p>

30 <p>The<a>remainder</a>is calculated as 12 - (9×1) = 3</p>

32 <p>The remainder is 3, not zero, so continue the process</p>

31 <p>The remainder is 3, not zero, so continue the process</p>

33 <p><strong>Step 2:</strong>Now divide the previous divisor (9) by the previous remainder (3)</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (9) by the previous remainder (3)</p>

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

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

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

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

36 <p>The GCF of 9 and 12 is 3.</p>

35 <p>The GCF of 9 and 12 is 3.</p>

37 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 12</h2>

36 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 12</h2>

38 <p>Finding GCF of 9 and 12 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

37 <p>Finding GCF of 9 and 12 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

39 <h3>Problem 1</h3>

38 <h3>Problem 1</h3>

40 <p>A teacher has 9 markers and 12 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>

39 <p>A teacher has 9 markers and 12 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>Okay, lets begin</p>

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

42 <p>We should find the GCF of 9 and 12 GCF of 9 and 12 3</p>

41 <p>We should find the GCF of 9 and 12 GCF of 9 and 12 3</p>

43 <p>There are 3 equal groups 9 ÷ 3 = 3 12 ÷ 3 = 4</p>

42 <p>There are 3 equal groups 9 ÷ 3 = 3 12 ÷ 3 = 4</p>

44 <p>There will be 3 groups, and each group gets 3 markers and 4 notebooks.</p>

43 <p>There will be 3 groups, and each group gets 3 markers and 4 notebooks.</p>

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

46 <p>As the GCF of 9 and 12 is 3, the teacher can make 3 groups.</p>

45 <p>As the GCF of 9 and 12 is 3, the teacher can make 3 groups.</p>

47 <p>Now divide 9 and 12 by 3.</p>

46 <p>Now divide 9 and 12 by 3.</p>

48 <p>Each group gets 3 markers and 4 notebooks.</p>

47 <p>Each group gets 3 markers and 4 notebooks.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 2</h3>

49 <h3>Problem 2</h3>

51 <p>A school has 9 green chairs and 12 yellow 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>

50 <p>A school has 9 green chairs and 12 yellow 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>

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

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

53 <p>GCF of 9 and 12 3 So each row will have 3 chairs.</p>

52 <p>GCF of 9 and 12 3 So each row will have 3 chairs.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>There are 9 green and 12 yellow chairs.</p>

54 <p>There are 9 green and 12 yellow chairs.</p>

56 <p>To find the total number of chairs in each row, we should find the GCF of 9 and 12.</p>

55 <p>To find the total number of chairs in each row, we should find the GCF of 9 and 12.</p>

57 <p>There will be 3 chairs in each row.</p>

56 <p>There will be 3 chairs in each row.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 3</h3>

58 <h3>Problem 3</h3>

60 <p>A tailor has 9 meters of silk ribbon and 12 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>

59 <p>A tailor has 9 meters of silk ribbon and 12 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>

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

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

62 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 12</p>

61 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 12</p>

63 <p>The GCF of 9 and 12 3</p>

62 <p>The GCF of 9 and 12 3</p>

64 <p>The ribbon is 3 meters long.</p>

63 <p>The ribbon is 3 meters long.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 9 and 12, which is 3.</p>

65 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 9 and 12, which is 3.</p>

67 <p>The length of each piece of the ribbon will be 3 meters.</p>

66 <p>The length of each piece of the ribbon will be 3 meters.</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h3>Problem 4</h3>

68 <h3>Problem 4</h3>

70 <p>A carpenter has two wooden planks, one 9 cm long and the other 12 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>

69 <p>A carpenter has two wooden planks, one 9 cm long and the other 12 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>

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

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

72 <p>The carpenter needs the longest piece of wood GCF of 9 and 12 3 The longest length of each piece is 3 cm.</p>

71 <p>The carpenter needs the longest piece of wood GCF of 9 and 12 3 The longest length of each piece is 3 cm.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 12 cm, respectively.</p>

73 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 12 cm, respectively.</p>

75 <p>We have to find the GCF of 9 and 12, which is 3 cm.</p>

74 <p>We have to find the GCF of 9 and 12, which is 3 cm.</p>

76 <p>The longest length of each piece is 3 cm.</p>

75 <p>The longest length of each piece is 3 cm.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h3>Problem 5</h3>

77 <h3>Problem 5</h3>

79 <p>If the GCF of 9 and ‘a’ is 3, and the LCM is 36. Find ‘a’.</p>

78 <p>If the GCF of 9 and ‘a’ is 3, and the LCM is 36. Find ‘a’.</p>

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

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

81 <p>The value of ‘a’ is 12.</p>

80 <p>The value of ‘a’ is 12.</p>

82 <h3>Explanation</h3>

81 <h3>Explanation</h3>

83 <p>GCF x LCM = product of the numbers 3 × 36 = 9 × a</p>

82 <p>GCF x LCM = product of the numbers 3 × 36 = 9 × a</p>

84 <p>108 = 9a</p>

83 <p>108 = 9a</p>

85 <p>a = 108 ÷ 9 = 12</p>

84 <p>a = 108 ÷ 9 = 12</p>

86 <p>Well explained 👍</p>

85 <p>Well explained 👍</p>

87 <h2>FAQs on the Greatest Common Factor of 9 and 12</h2>

86 <h2>FAQs on the Greatest Common Factor of 9 and 12</h2>

88 <h3>1.What is the LCM of 9 and 12?</h3>

87 <h3>1.What is the LCM of 9 and 12?</h3>

89 <p>The LCM of 9 and 12 is 36.</p>

88 <p>The LCM of 9 and 12 is 36.</p>

90 <h3>2.Is 9 divisible by 2?</h3>

89 <h3>2.Is 9 divisible by 2?</h3>

91 <p>No, 9 is not divisible by 2 because it is an odd number.</p>

90 <p>No, 9 is not divisible by 2 because it is an odd number.</p>

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

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

93 <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>

92 <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>

94 <h3>4.What is the prime factorization of 12?</h3>

93 <h3>4.What is the prime factorization of 12?</h3>

95 <p>The prime factorization of 12 is 2² x 3.</p>

94 <p>The prime factorization of 12 is 2² x 3.</p>

96 <h3>5.Are 9 and 12 prime numbers?</h3>

95 <h3>5.Are 9 and 12 prime numbers?</h3>

97 <p>No, 9 and 12 are not prime numbers because both of them have more than two factors.</p>

96 <p>No, 9 and 12 are not prime numbers because both of them have more than two factors.</p>

98 <h2>Important Glossaries for GCF of 9 and 12</h2>

97 <h2>Important Glossaries for GCF of 9 and 12</h2>

99 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

98 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

100 <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>

99 <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>

101 <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 factor of 9 is 3.</li>

100 <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 factor of 9 is 3.</li>

102 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 5, the remainder is 2 and the quotient is 2.</li>

101 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 5, the remainder is 2 and the quotient is 2.</li>

103 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 9 and 12 is 36.</li>

102 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 9 and 12 is 36.</li>

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

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

105 <p>▶</p>

104 <p>▶</p>

106 <h2>Hiralee Lalitkumar Makwana</h2>

105 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h3>About the Author</h3>

106 <h3>About the Author</h3>

108 <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>

107 <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>

109 <h3>Fun Fact</h3>

108 <h3>Fun Fact</h3>

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

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