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2 <p>Last updated on<strong>September 18, 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 3 and 12.</p>

4 <h2>What is the GCF of 3 and 12?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>3 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.</p>

6 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 3 and 12?</h2>

8 <p>To find the GCF of 3 and 12, 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><h2>GCF of 3 and 12 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 3 and 12 using the listing of<a>factors</a></p>

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

15 <p>Factors of 3 = 1, 3.</p>

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

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

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 3. The GCF of 3 and 12 is 3.</p>

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21 <h2>GCF of 3 and 12 Using Prime Factorization</h2>

20 <h2>GCF of 3 and 12 Using Prime Factorization</h2>

22 <p>To find the GCF of 3 and 12 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 3 and 12 using the Prime Factorization Method, follow these steps:</p>

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

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

24 <p>Prime Factors of 3: 3 = 3</p>

23 <p>Prime Factors of 3: 3 = 3</p>

25 <p>Prime Factors of 12: 12 = 2 × 2 × 3</p>

24 <p>Prime Factors of 12: 12 = 2 × 2 × 3</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 3.</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 3.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 3 and 12 is 3.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 3 and 12 is 3.</p>

28 <h2>GCF of 3 and 12 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 3 and 12 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 3 and 12 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 3 and 12 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

31 <p>Here, divide 12 by 3 12 ÷ 3 = 4 (<a>quotient</a>),<a>remainder</a>= 0</p>

30 <p>Here, divide 12 by 3 12 ÷ 3 = 4 (<a>quotient</a>),<a>remainder</a>= 0</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 3 and 12 is 3.</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 3 and 12 is 3.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 3 and 12</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 3 and 12</h2>

34 <p>Finding the GCF of 3 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>

33 <p>Finding the GCF of 3 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>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A chef has 3 kilograms of flour and 12 kilograms of sugar. He wants to package them into equal sets, with the largest number of kilograms in each package. How many kilograms will each package contain?</p>

35 <p>A chef has 3 kilograms of flour and 12 kilograms of sugar. He wants to package them into equal sets, with the largest number of kilograms in each package. How many kilograms will each package contain?</p>

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

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

38 <p>We should find the GCF of 3 and 12 GCF of 3 and 12 is 3.</p>

37 <p>We should find the GCF of 3 and 12 GCF of 3 and 12 is 3.</p>

39 <p>There are 3 equal packages. 3 ÷ 3 = 1 12 ÷ 3 = 4</p>

38 <p>There are 3 equal packages. 3 ÷ 3 = 1 12 ÷ 3 = 4</p>

40 <p>There will be 3 packages, and each package gets 1 kilogram of flour and 4 kilograms of sugar.</p>

39 <p>There will be 3 packages, and each package gets 1 kilogram of flour and 4 kilograms of sugar.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 3 and 12 is 3, the chef can make 3 packages.</p>

41 <p>As the GCF of 3 and 12 is 3, the chef can make 3 packages.</p>

43 <p>Now divide 3 and 12 by 3.</p>

42 <p>Now divide 3 and 12 by 3.</p>

44 <p>Each package gets 1 kilogram of flour and 4 kilograms of sugar.</p>

43 <p>Each package gets 1 kilogram of flour and 4 kilograms of sugar.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>A gardener has 3 rose bushes and 12 lily bushes. They want to arrange them in rows with the same number of bushes in each row, using the largest possible number of bushes per row. How many bushes will be in each row?</p>

46 <p>A gardener has 3 rose bushes and 12 lily bushes. They want to arrange them in rows with the same number of bushes in each row, using the largest possible number of bushes per row. How many bushes will be in each row?</p>

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

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

49 <p>GCF of 3 and 12 is 3. So each row will have 3 bushes.</p>

48 <p>GCF of 3 and 12 is 3. So each row will have 3 bushes.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>There are 3 rose bushes and 12 lily bushes.</p>

50 <p>There are 3 rose bushes and 12 lily bushes.</p>

52 <p>To find the total number of bushes in each row, we should find the GCF of 3 and 12.</p>

51 <p>To find the total number of bushes in each row, we should find the GCF of 3 and 12.</p>

53 <p>There will be 3 bushes in each row.</p>

52 <p>There will be 3 bushes in each row.</p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

54 <h3>Problem 3</h3>

56 <p>A painter has 3 meters of red paint and 12 meters of blue paint. He wants to use both paints in pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

55 <p>A painter has 3 meters of red paint and 12 meters of blue paint. He wants to use both paints in pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

58 <p>For calculating the longest equal length, we have to calculate the GCF of 3 and 12</p>

57 <p>For calculating the longest equal length, we have to calculate the GCF of 3 and 12</p>

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

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

60 <p>The paint is 3 meters long.</p>

59 <p>The paint is 3 meters long.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

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

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

63 <p>The length of each piece of paint will be 3 meters.</p>

62 <p>The length of each piece of paint will be 3 meters.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

64 <h3>Problem 4</h3>

66 <p>A craftsman has two ropes, one 3 meters long and the other 12 meters long. He wants to cut them into the longest possible equal pieces, without any rope left over. What should be the length of each piece?</p>

65 <p>A craftsman has two ropes, one 3 meters long and the other 12 meters long. He wants to cut them into the longest possible equal pieces, without any rope left over. What should be the length of each piece?</p>

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

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

68 <p>The craftsman needs the longest piece of rope GCF of 3 and 12 is 3.</p>

67 <p>The craftsman needs the longest piece of rope GCF of 3 and 12 is 3.</p>

69 <p>The longest length of each piece is 3 meters.</p>

68 <p>The longest length of each piece is 3 meters.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>To find the longest length of each piece of the two ropes, 3 meters and 12 meters respectively, we have to find the GCF of 3 and 12, which is 3 meters.</p>

70 <p>To find the longest length of each piece of the two ropes, 3 meters and 12 meters respectively, we have to find the GCF of 3 and 12, which is 3 meters.</p>

72 <p>The longest length of each piece is 3 meters.</p>

71 <p>The longest length of each piece is 3 meters.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

73 <h3>Problem 5</h3>

75 <p>If the GCF of 3 and ‘b’ is 3, and the LCM is 12. Find ‘b’.</p>

74 <p>If the GCF of 3 and ‘b’ is 3, and the LCM is 12. Find ‘b’.</p>

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

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

77 <p>The value of ‘b’ is 12.</p>

76 <p>The value of ‘b’ is 12.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>GCF × LCM = product of the numbers</p>

78 <p>GCF × LCM = product of the numbers</p>

80 <p>3 × 12 = 3 × b</p>

79 <p>3 × 12 = 3 × b</p>

81 <p>36 = 3b</p>

80 <p>36 = 3b</p>

82 <p>b = 36 ÷ 3 = 12</p>

81 <p>b = 36 ÷ 3 = 12</p>

83 <p>Well explained 👍</p>

82 <p>Well explained 👍</p>

84 <h2>FAQs on the Greatest Common Factor of 3 and 12</h2>

83 <h2>FAQs on the Greatest Common Factor of 3 and 12</h2>

85 <h3>1.What is the LCM of 3 and 12?</h3>

84 <h3>1.What is the LCM of 3 and 12?</h3>

86 <p>The LCM of 3 and 12 is 12.</p>

85 <p>The LCM of 3 and 12 is 12.</p>

87 <h3>2.Is 3 divisible by 2?</h3>

86 <h3>2.Is 3 divisible by 2?</h3>

88 <p>No, 3 is not divisible by 2 because it is an odd number.</p>

87 <p>No, 3 is not divisible by 2 because it is an odd number.</p>

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

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

90 <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>

89 <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>

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

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

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

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

93 <h3>5.Are 3 and 12 prime numbers?</h3>

92 <h3>5.Are 3 and 12 prime numbers?</h3>

94 <p>No, 3 is a prime number, but 12 is not a prime number because it has more than two factors.</p>

93 <p>No, 3 is a prime number, but 12 is not a prime number because it has more than two factors.</p>

95 <h2>Important Glossaries for GCF of 3 and 12</h2>

94 <h2>Important Glossaries for GCF of 3 and 12</h2>

96 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

95 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

97 </ul><ul><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, and so on.</li>

96 </ul><ul><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, and so on.</li>

98 </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 12 are 2 and 3.</li>

97 </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 12 are 2 and 3.</li>

99 </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 and the quotient is 3.</li>

98 </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 and the quotient is 3.</li>

100 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 12 is 12.</li>

99 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 12 is 12.</li>

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

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

102 <p>▶</p>

101 <p>▶</p>

103 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h2>Hiralee Lalitkumar Makwana</h2>

104 <h3>About the Author</h3>

103 <h3>About the Author</h3>

105 <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>

104 <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>

106 <h3>Fun Fact</h3>

105 <h3>Fun Fact</h3>

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

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