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2 <p>Last updated on<strong>August 11, 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 12 and 48.</p>

4 <h2>What is the GCF of 12 and 48?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>12 and 48 is 12. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>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>

7 <h2>How to find the GCF of 12 and 48?</h2>

8 <p>To find the GCF of 12 and 48, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

9 <h2>GCF of 12 and 48 by Using Listing of Factors</h2>

10 <p>Steps to find the GCF of 12 and 48 using the listing of<a>factors</a></p>

11 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 12 = 1, 2, 3, 4, 6, 12. Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.</p>

12 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 12 and 48: 1, 2, 3, 4, 6, 12.</p>

13 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 12. The GCF of 12 and 48 is 12.</p>

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16 <h2>GCF of 12 and 48 Using Prime Factorization</h2>

15 <h2>GCF of 12 and 48 Using Prime Factorization</h2>

17 <p>To find the GCF of 12 and 48 using the Prime Factorization Method, follow these steps:</p>

16 <p>To find the GCF of 12 and 48 using the Prime Factorization Method, follow these steps:</p>

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

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

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

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

20 <p>Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3</p>

19 <p>Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 2² x 3</p>

20 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 2² x 3</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 2² x 3 = 4 x 3 = 12.</p>

21 <p><strong>Step 3:</strong>Multiply the common prime factors 2² x 3 = 4 x 3 = 12.</p>

23 <p>The Greatest Common Factor of 12 and 48 is 12.</p>

22 <p>The Greatest Common Factor of 12 and 48 is 12.</p>

24 <h2>GCF of 12 and 48 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 12 and 48 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 12 and 48 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 12 and 48 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p>Step 1: First, divide the larger number by the smaller number Here, divide 48 by 12 48 ÷ 12 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 48 - (12 x 4) = 0</p>

25 <p>Step 1: First, divide the larger number by the smaller number Here, divide 48 by 12 48 ÷ 12 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 48 - (12 x 4) = 0</p>

27 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 12 and 48 is 12.</p>

26 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 12 and 48 is 12.</p>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 12 and 48</h2>

27 <h2>Common Mistakes and How to Avoid Them in GCF of 12 and 48</h2>

29 <p>Finding the GCF of 12 and 48 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

28 <p>Finding the GCF of 12 and 48 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>A chef has 12 apples and 48 oranges. She wants to arrange them into baskets with equal quantities of each fruit in each basket. How many fruits will be in each basket?</p>

30 <p>A chef has 12 apples and 48 oranges. She wants to arrange them into baskets with equal quantities of each fruit in each basket. How many fruits will be in each basket?</p>

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

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

33 <p>We should find the GCF of 12 and 48. GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. There are 12 equal baskets.</p>

32 <p>We should find the GCF of 12 and 48. GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. There are 12 equal baskets.</p>

34 <p>12 ÷ 12 = 1</p>

33 <p>12 ÷ 12 = 1</p>

35 <p>48 ÷ 12 = 4</p>

34 <p>48 ÷ 12 = 4</p>

36 <p>There will be 12 baskets, and each basket gets 1 apple and 4 oranges.</p>

35 <p>There will be 12 baskets, and each basket gets 1 apple and 4 oranges.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>As the GCF of 12 and 48 is 12, the chef can make 12 baskets. Now divide 12 and 48 by 12. Each basket gets 1 apple and 4 oranges.</p>

37 <p>As the GCF of 12 and 48 is 12, the chef can make 12 baskets. Now divide 12 and 48 by 12. Each basket gets 1 apple and 4 oranges.</p>

39 <p>Well explained 👍</p>

38 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

39 <h3>Problem 2</h3>

41 <p>A sports club has 12 basketballs and 48 volleyballs. They want to distribute them into boxes with the same number of balls in each box, using the largest possible number of balls per box. How many balls will be in each box?</p>

40 <p>A sports club has 12 basketballs and 48 volleyballs. They want to distribute them into boxes with the same number of balls in each box, using the largest possible number of balls per box. How many balls will be in each box?</p>

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

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

43 <p>GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. So each box will have 12 balls.</p>

42 <p>GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. So each box will have 12 balls.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>There are 12 basketballs and 48 volleyballs. To find the total number of balls in each box, we should find the GCF of 12 and 48. There will be 12 balls in each box.</p>

44 <p>There are 12 basketballs and 48 volleyballs. To find the total number of balls in each box, we should find the GCF of 12 and 48. There will be 12 balls in each box.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>A tailor has 12 meters of red fabric and 48 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>

47 <p>A tailor has 12 meters of red fabric and 48 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>

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

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

50 <p>For calculating the longest equal length, we have to calculate the GCF of 12 and 48. The GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. The fabric is 12 meters long.</p>

49 <p>For calculating the longest equal length, we have to calculate the GCF of 12 and 48. The GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. The fabric is 12 meters long.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 12 and 48, which is 12. The length of each piece of fabric will be 12 meters.</p>

51 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 12 and 48, which is 12. The length of each piece of fabric will be 12 meters.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>A carpenter has two wooden planks, one 12 cm long and the other 48 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>

54 <p>A carpenter has two wooden planks, one 12 cm long and the other 48 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>

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

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

57 <p>The carpenter needs the longest piece of wood. GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. The longest length of each piece is 12 cm.</p>

56 <p>The carpenter needs the longest piece of wood. GCF of 12 and 48: 2² x 3 = 4 x 3 = 12. The longest length of each piece is 12 cm.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the longest length of each piece of the two wooden planks, 12 cm and 48 cm, respectively, we have to find the GCF of 12 and 48, which is 12 cm. The longest length of each piece is 12 cm.</p>

58 <p>To find the longest length of each piece of the two wooden planks, 12 cm and 48 cm, respectively, we have to find the GCF of 12 and 48, which is 12 cm. The longest length of each piece is 12 cm.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 5</h3>

60 <h3>Problem 5</h3>

62 <p>If the GCF of 12 and ‘a’ is 12, and the LCM is 48, find ‘a’.</p>

61 <p>If the GCF of 12 and ‘a’ is 12, and the LCM is 48, find ‘a’.</p>

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

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

64 <p>The value of ‘a’ is 48.</p>

63 <p>The value of ‘a’ is 48.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>GCF x LCM = product of the numbers 12 x 48 = 12 x a</p>

65 <p>GCF x LCM = product of the numbers 12 x 48 = 12 x a</p>

67 <p>576 = 12a</p>

66 <p>576 = 12a</p>

68 <p>a = 576 ÷ 12 = 48</p>

67 <p>a = 576 ÷ 12 = 48</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQs on the Greatest Common Factor of 12 and 48</h2>

69 <h2>FAQs on the Greatest Common Factor of 12 and 48</h2>

71 <h3>1.What is the LCM of 12 and 48?</h3>

70 <h3>1.What is the LCM of 12 and 48?</h3>

72 <p>The LCM of 12 and 48 is 48.</p>

71 <p>The LCM of 12 and 48 is 48.</p>

73 <h3>2.Is 12 divisible by 2?</h3>

72 <h3>2.Is 12 divisible by 2?</h3>

74 <p>Yes, 12 is divisible by 2 because it is an even number.</p>

73 <p>Yes, 12 is divisible by 2 because it is an even number.</p>

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

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

76 <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>

75 <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>

77 <h3>4.What is the prime factorization of 48?</h3>

76 <h3>4.What is the prime factorization of 48?</h3>

78 <p>The prime factorization of 48 is 2⁴ x 3.</p>

77 <p>The prime factorization of 48 is 2⁴ x 3.</p>

79 <h3>5.Are 12 and 48 prime numbers?</h3>

78 <h3>5.Are 12 and 48 prime numbers?</h3>

80 <p>No, 12 and 48 are not prime numbers because both of them have more than two factors.</p>

79 <p>No, 12 and 48 are not prime numbers because both of them have more than two factors.</p>

81 <h2>Important Glossaries for GCF of 12 and 48</h2>

80 <h2>Important Glossaries for GCF of 12 and 48</h2>

82 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>

81 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>

83 </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>

82 </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>

84 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.</li>

83 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.</li>

85 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 48 is 48.</li>

84 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 48 is 48.</li>

86 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 48 is 12, as it is their largest common factor that divides the numbers completely.</li>

85 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 48 is 12, as it is their largest common factor that divides the numbers completely.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Hiralee Lalitkumar Makwana</h2>

88 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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>

90 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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