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2 <p>Last updated on<strong>August 13, 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 75 and 48.</p>

4 <h2>What is the GCF of 75 and 48?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>75 and 48 is 3. 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, which are always positive.</p>

7 <h2>How to find the GCF of 75 and 48?</h2>

8 <p>To find the GCF of 75 and 48, a few methods are described below -</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

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

12 </ol><h2>GCF of 75 and 48 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 75 and 48 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 75 = 1, 3, 5, 15, 25, 75.</p>

16 <p>Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 75 and 48: 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 75 and 48 is 3.</p>

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21 <h2>GCF of 75 and 48 Using Prime Factorization</h2>

20 <h2>GCF of 75 and 48 Using Prime Factorization</h2>

22 <p>To find the GCF of 75 and 48 using Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 75 and 48 using Prime Factorization Method, follow these steps:</p>

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

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

24 <p>Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²</p>

23 <p>Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²</p>

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

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

26 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>The common prime factors are: 3</p>

25 <p><strong>Step 2:</strong>Now, identify the common<a>prime factors</a>The common prime factors are: 3</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 3 The Greatest Common Factor of 75 and 48 is 3.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 3 The Greatest Common Factor of 75 and 48 is 3.</p>

28 <h2>GCF of 75 and 48 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 75 and 48 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 75 and 48 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 75 and 48 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 Here, divide 75 by 48 75 ÷ 48 = 1 (<a>quotient</a>) The<a>remainder</a>is calculated as 75 - (48×1) = 27 The remainder is 27, not zero, so continue the process</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 75 by 48 75 ÷ 48 = 1 (<a>quotient</a>) The<a>remainder</a>is calculated as 75 - (48×1) = 27 The remainder is 27, not zero, so continue the process</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (48) by the previous remainder (27) Divide 48 by 27 48 ÷ 27 = 1 (quotient), remainder = 48 - (27×1) = 21 The remainder is 21, not zero, so continue the process</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (48) by the previous remainder (27) Divide 48 by 27 48 ÷ 27 = 1 (quotient), remainder = 48 - (27×1) = 21 The remainder is 21, not zero, so continue the process</p>

32 <p><strong>Step 3:</strong>Now divide the previous divisor (27) by the previous remainder (21) Divide 27 by 21 27 ÷ 21 = 1 (quotient), remainder = 27 - (21×1) = 6 The remainder is 6, not zero, so continue the process</p>

31 <p><strong>Step 3:</strong>Now divide the previous divisor (27) by the previous remainder (21) Divide 27 by 21 27 ÷ 21 = 1 (quotient), remainder = 27 - (21×1) = 6 The remainder is 6, not zero, so continue the process</p>

33 <p><strong>Step 4:</strong>Now divide the previous divisor (21) by the previous remainder (6) Divide 21 by 6 21 ÷ 6 = 3 (quotient), remainder = 21 - (6×3) = 3 The remainder is 3, not zero, so continue the process</p>

32 <p><strong>Step 4:</strong>Now divide the previous divisor (21) by the previous remainder (6) Divide 21 by 6 21 ÷ 6 = 3 (quotient), remainder = 21 - (6×3) = 3 The remainder is 3, not zero, so continue the process</p>

34 <p><strong>Step 5:</strong>Now divide the previous divisor (6) by the previous remainder (3) Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

33 <p><strong>Step 5:</strong>Now divide the previous divisor (6) by the previous remainder (3) Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

35 <p>The remainder is zero, the divisor will become the GCF. The GCF of 75 and 48 is 3.</p>

34 <p>The remainder is zero, the divisor will become the GCF. The GCF of 75 and 48 is 3.</p>

36 <h2>Common Mistakes and How to Avoid Them in GCF of 75 and 48</h2>

35 <h2>Common Mistakes and How to Avoid Them in GCF of 75 and 48</h2>

37 <p>Finding GCF of 75 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>

36 <p>Finding GCF of 75 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>

38 <h3>Problem 1</h3>

37 <h3>Problem 1</h3>

39 <p>A gardener has 75 roses and 48 tulips. She wants to plant them in rows with the largest number of flowers in each row. How many flowers will be in each row?</p>

38 <p>A gardener has 75 roses and 48 tulips. She wants to plant them in rows with the largest number of flowers in each row. How many flowers will be in each row?</p>

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

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

41 <p>We should find GCF of 75 and 48 GCF of 75 and 48 3</p>

40 <p>We should find GCF of 75 and 48 GCF of 75 and 48 3</p>

42 <p>There are 3 equal groups 75 ÷ 3 = 25 48 ÷ 3 = 16</p>

41 <p>There are 3 equal groups 75 ÷ 3 = 25 48 ÷ 3 = 16</p>

43 <p>There will be 3 groups, and each group gets 25 roses and 16 tulips.</p>

42 <p>There will be 3 groups, and each group gets 25 roses and 16 tulips.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>As the GCF of 75 and 48 is 3, the gardener can make 3 groups. Now divide 75 and 48 by 3. Each group gets 25 roses and 16 tulips.</p>

44 <p>As the GCF of 75 and 48 is 3, the gardener can make 3 groups. Now divide 75 and 48 by 3. Each group gets 25 roses and 16 tulips.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 2</h3>

46 <h3>Problem 2</h3>

48 <p>A chef has 75 apples and 48 oranges. He wants to create fruit baskets with the largest possible number of fruits in each basket. How many fruits will be in each basket?</p>

47 <p>A chef has 75 apples and 48 oranges. He wants to create fruit baskets with the largest possible number of fruits in each basket. How many fruits will be in each basket?</p>

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

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

50 <p>GCF of 75 and 48 3 So each basket will have 3 fruits.</p>

49 <p>GCF of 75 and 48 3 So each basket will have 3 fruits.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>There are 75 apples and 48 oranges. To find the total number of fruits in each basket, we should find the GCF of 75 and 48. There will be 3 fruits in each basket.</p>

51 <p>There are 75 apples and 48 oranges. To find the total number of fruits in each basket, we should find the GCF of 75 and 48. There will be 3 fruits in each basket.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

53 <h3>Problem 3</h3>

55 <p>A tailor has 75 meters of fabric A and 48 meters of fabric B. He wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

54 <p>A tailor has 75 meters of fabric A and 48 meters of fabric B. He wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

57 <p>For calculating longest equal length, we have to calculate the GCF of 75 and 48 The GCF of 75 and 48 3 The fabric is 3 meters long.</p>

56 <p>For calculating longest equal length, we have to calculate the GCF of 75 and 48 The GCF of 75 and 48 3 The fabric is 3 meters long.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 48 which is 3. The length of each piece of the fabric will be 3 meters.</p>

58 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 48 which is 3. The length of each piece of the fabric will be 3 meters.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

60 <h3>Problem 4</h3>

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

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

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

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

64 <p>The carpenter needs the longest piece of wood GCF of 75 and 48 3 The longest length of each piece is 3 cm.</p>

63 <p>The carpenter needs the longest piece of wood GCF of 75 and 48 3 The longest length of each piece is 3 cm.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the longest length of each piece of the two wooden planks, 75 cm and 48 cm, respectively. We have to find the GCF of 75 and 48, which is 3 cm. The longest length of each piece is 3 cm.</p>

65 <p>To find the longest length of each piece of the two wooden planks, 75 cm and 48 cm, respectively. We have to find the GCF of 75 and 48, which is 3 cm. The longest length of each piece is 3 cm.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

67 <h3>Problem 5</h3>

69 <p>If the GCF of 75 and ‘b’ is 15, and the LCM is 300. Find ‘b’.</p>

68 <p>If the GCF of 75 and ‘b’ is 15, and the LCM is 300. Find ‘b’.</p>

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

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

71 <p>The value of ‘b’ is 60.</p>

70 <p>The value of ‘b’ is 60.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

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

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

74 <p>15 × 300 = 75 × b</p>

73 <p>15 × 300 = 75 × b</p>

75 <p>4500 = 75b</p>

74 <p>4500 = 75b</p>

76 <p>b = 4500 ÷ 75 = 60</p>

75 <p>b = 4500 ÷ 75 = 60</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQs on the Greatest Common Factor of 75 and 48</h2>

77 <h2>FAQs on the Greatest Common Factor of 75 and 48</h2>

79 <h3>1.What is the LCM of 75 and 48?</h3>

78 <h3>1.What is the LCM of 75 and 48?</h3>

80 <p>The LCM of 75 and 48 is 1200.</p>

79 <p>The LCM of 75 and 48 is 1200.</p>

81 <h3>2.Is 75 divisible by 3?</h3>

80 <h3>2.Is 75 divisible by 3?</h3>

82 <p>Yes, 75 is divisible by 3 because the<a>sum</a>of its digits (7+5=12) is divisible by 3.</p>

81 <p>Yes, 75 is divisible by 3 because the<a>sum</a>of its digits (7+5=12) is divisible by 3.</p>

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

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

84 <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>

83 <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>

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

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

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

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

87 <h3>5.Are 75 and 48 prime numbers?</h3>

86 <h3>5.Are 75 and 48 prime numbers?</h3>

88 <p>No, 75 and 48 are not prime numbers because both of them have more than two factors.</p>

87 <p>No, 75 and 48 are not prime numbers because both of them have more than two factors.</p>

89 <h2>Important Glossaries for GCF of 75 and 48</h2>

88 <h2>Important Glossaries for GCF of 75 and 48</h2>

90 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</li>

89 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</li>

91 </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 20 are 2 and 5.</li>

90 </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 20 are 2 and 5.</li>

92 </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.</li>

91 </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.</li>

93 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 75 and 48 is 1200.</li>

92 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 75 and 48 is 1200.</li>

94 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 75 and 48 will be 3, as it is their largest common factor that divides the numbers completely.</li>

93 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 75 and 48 will be 3, as it is their largest common factor that divides the numbers completely.</li>

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

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

96 <p>▶</p>

95 <p>▶</p>

97 <h2>Hiralee Lalitkumar Makwana</h2>

96 <h2>Hiralee Lalitkumar Makwana</h2>

98 <h3>About the Author</h3>

97 <h3>About the Author</h3>

99 <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>

98 <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>

100 <h3>Fun Fact</h3>

99 <h3>Fun Fact</h3>

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

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