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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 to schedule events. In this topic, we will learn about the GCF of 10 and 12.</p>

4 <h2>What is the GCF of 10 and 12?</h2>

5 <p>The<a>greatest common factor</a>of 10 and 12 is 2. 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 10 and 12?</h2>

7 <p>To find the GCF of 10 and 12, a few methods are described below -</p>

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

9 <li>Prime Factorization</li>

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

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

12 <p>Steps to find the GCF of 10 and 12 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 10 = 1, 2, 5, 10.</p>

15 <p>Factors of 12 = 1, 2, 3, 4, 6, 12.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 10 and 12: 1, 2.</p>

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

18 <p>The largest factor that both numbers have is 2.</p>

19 <p>The GCF of 10 and 12 is 2.</p>

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22 <h2>GCF of 10 and 12 Using Prime Factorization</h2>

21 <h2>GCF of 10 and 12 Using Prime Factorization</h2>

23 <p>To find the GCF of 10 and 12 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 10 and 12 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 10: 10 = 2 x 5</p>

24 <p>Prime Factors of 10: 10 = 2 x 5</p>

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

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

27 <p>The common prime factor is: 2</p>

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

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

30 <p>The Greatest Common Factor of 10 and 12 is 2.</p>

29 <p>The Greatest Common Factor of 10 and 12 is 2.</p>

31 <h2>GCF of 10 and 12 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 10 and 12 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 10 and 12 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 10 and 12 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 12 by 10 12 ÷ 10 = 1 (<a>quotient</a>),</p>

33 <p>Here, divide 12 by 10 12 ÷ 10 = 1 (<a>quotient</a>),</p>

35 <p>The<a>remainder</a>is calculated as 12-(10×1)=2</p>

34 <p>The<a>remainder</a>is calculated as 12-(10×1)=2</p>

36 <p>The remainder is 2, not zero, so continue the process</p>

35 <p>The remainder is 2, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (10) by the previous remainder (2)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (10) by the previous remainder (2)</p>

38 <p>Divide 10 by 2 10 ÷ 2 = 5 (quotient), remainder = 10-(2×5)=0</p>

37 <p>Divide 10 by 2 10 ÷ 2 = 5 (quotient), remainder = 10-(2×5)=0</p>

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

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

40 <p>The GCF of 10 and 12 is 2.</p>

39 <p>The GCF of 10 and 12 is 2.</p>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 12</h2>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 12</h2>

42 <p>Finding GCF of 10 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>

41 <p>Finding GCF of 10 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>

43 <h3>Problem 1</h3>

42 <h3>Problem 1</h3>

44 <p>A gardener has 10 tulips and 12 roses. She wants to group them into equal flower arrangements, with the largest number of flowers in each group. How many flowers will be in each group?</p>

43 <p>A gardener has 10 tulips and 12 roses. She wants to group them into equal flower arrangements, with the largest number of flowers in each group. How many flowers will be in each group?</p>

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

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

46 <p>We should find the GCF of 10 and 12 GCF of 10 and 12 2</p>

45 <p>We should find the GCF of 10 and 12 GCF of 10 and 12 2</p>

47 <p>There are 2 equal groups 10 ÷ 2 = 5 12 ÷ 2 = 6</p>

46 <p>There are 2 equal groups 10 ÷ 2 = 5 12 ÷ 2 = 6</p>

48 <p>There will be 2 groups, and each group gets 5 tulips and 6 roses.</p>

47 <p>There will be 2 groups, and each group gets 5 tulips and 6 roses.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>As the GCF of 10 and 12 is 2, the gardener can make 2 groups.</p>

49 <p>As the GCF of 10 and 12 is 2, the gardener can make 2 groups.</p>

51 <p>Now divide 10 and 12 by 2.</p>

50 <p>Now divide 10 and 12 by 2.</p>

52 <p>Each group gets 5 tulips and 6 roses.</p>

51 <p>Each group gets 5 tulips and 6 roses.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 2</h3>

53 <h3>Problem 2</h3>

55 <p>A party planner has 10 red balloons and 12 blue balloons. They want to arrange them in clusters with the same number of balloons in each cluster, using the largest possible number of balloons per cluster. How many balloons will be in each cluster?</p>

54 <p>A party planner has 10 red balloons and 12 blue balloons. They want to arrange them in clusters with the same number of balloons in each cluster, using the largest possible number of balloons per cluster. How many balloons will be in each cluster?</p>

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

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

57 <p>GCF of 10 and 12 2</p>

56 <p>GCF of 10 and 12 2</p>

58 <p>So each cluster will have 2 balloons.</p>

57 <p>So each cluster will have 2 balloons.</p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>There are 10 red and 12 blue balloons.</p>

59 <p>There are 10 red and 12 blue balloons.</p>

61 <p>To find the total number of balloons in each cluster, we should find the GCF of 10 and 12.</p>

60 <p>To find the total number of balloons in each cluster, we should find the GCF of 10 and 12.</p>

62 <p>There will be 2 balloons in each cluster.</p>

61 <p>There will be 2 balloons in each cluster.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>A tailor has 10 meters of red fabric and 12 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>A tailor has 10 meters of red fabric and 12 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>

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

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

67 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 12</p>

66 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 12</p>

68 <p>The GCF of 10 and 12 2</p>

67 <p>The GCF of 10 and 12 2</p>

69 <p>The fabric is 2 meters long.</p>

68 <p>The fabric is 2 meters long.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 10 and 12, which is 2.</p>

70 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 10 and 12, which is 2.</p>

72 <p>The length of each piece of fabric will be 2 meters.</p>

71 <p>The length of each piece of fabric will be 2 meters.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 4</h3>

73 <h3>Problem 4</h3>

75 <p>A carpenter has two wooden planks, one 10 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>

74 <p>A carpenter has two wooden planks, one 10 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>

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

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

77 <p>The carpenter needs the longest piece of wood GCF of 10 and 12 2</p>

76 <p>The carpenter needs the longest piece of wood GCF of 10 and 12 2</p>

78 <p>The longest length of each piece is 2 cm.</p>

77 <p>The longest length of each piece is 2 cm.</p>

79 <h3>Explanation</h3>

78 <h3>Explanation</h3>

80 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 12 cm, respectively, we have to find the GCF of 10 and 12, which is 2 cm.</p>

79 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 12 cm, respectively, we have to find the GCF of 10 and 12, which is 2 cm.</p>

81 <p>The longest length of each piece is 2 cm.</p>

80 <p>The longest length of each piece is 2 cm.</p>

82 <p>Well explained 👍</p>

81 <p>Well explained 👍</p>

83 <h3>Problem 5</h3>

82 <h3>Problem 5</h3>

84 <p>If the GCF of 10 and ‘b’ is 2, and the LCM is 60. Find ‘b’.</p>

83 <p>If the GCF of 10 and ‘b’ is 2, and the LCM is 60. Find ‘b’.</p>

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

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

86 <p>The value of ‘b’ is 12.</p>

85 <p>The value of ‘b’ is 12.</p>

87 <h3>Explanation</h3>

86 <h3>Explanation</h3>

88 <p>GCF × LCM = product of the numbers 2 × 60 = 10 × b</p>

87 <p>GCF × LCM = product of the numbers 2 × 60 = 10 × b</p>

89 <p>120 = 10b</p>

88 <p>120 = 10b</p>

90 <p>b = 120 ÷ 10 = 12</p>

89 <p>b = 120 ÷ 10 = 12</p>

91 <p>Well explained 👍</p>

90 <p>Well explained 👍</p>

92 <h2>FAQs on the Greatest Common Factor of 10 and 12</h2>

91 <h2>FAQs on the Greatest Common Factor of 10 and 12</h2>

93 <h3>1.What is the LCM of 10 and 12?</h3>

92 <h3>1.What is the LCM of 10 and 12?</h3>

94 <p>The LCM of 10 and 12 is 60.</p>

93 <p>The LCM of 10 and 12 is 60.</p>

95 <h3>2.Is 10 divisible by 5?</h3>

94 <h3>2.Is 10 divisible by 5?</h3>

96 <p>Yes, 10 is divisible by 5 because 10 ÷ 5 = 2.</p>

95 <p>Yes, 10 is divisible by 5 because 10 ÷ 5 = 2.</p>

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

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

98 <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>

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>

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

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

100 <p>The prime factorization of 12 is 2² × 3.</p>

99 <p>The prime factorization of 12 is 2² × 3.</p>

101 <h3>5.Are 10 and 12 prime numbers?</h3>

100 <h3>5.Are 10 and 12 prime numbers?</h3>

102 <p>No, 10 and 12 are not prime numbers because both of them have more than two factors.</p>

101 <p>No, 10 and 12 are not prime numbers because both of them have more than two factors.</p>

103 <h2>Important Glossaries for GCF of 10 and 12</h2>

102 <h2>Important Glossaries for GCF of 10 and 12</h2>

104 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

103 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

105 <li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

104 <li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

106 <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 12 are 2 and 3.</li>

105 <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 12 are 2 and 3.</li>

107 <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>

106 <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>

108 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 12 is 60.</li>

107 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 12 is 60.</li>

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

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

110 <p>▶</p>

109 <p>▶</p>

111 <h2>Hiralee Lalitkumar Makwana</h2>

110 <h2>Hiralee Lalitkumar Makwana</h2>

112 <h3>About the Author</h3>

111 <h3>About the Author</h3>

113 <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>

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>

114 <h3>Fun Fact</h3>

113 <h3>Fun Fact</h3>

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

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