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2 <p>Last updated on<strong>September 12, 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 100.</p>

4 <h2>What is the GCF of 75 and 100?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>75 and 100 is 25. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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 75 and 100?</h2>

7 <p>To find the GCF of 75 and 100, a few methods are described below -</p>

8 <ol><li>Listing Factors</li>

9 <li>Prime Factorization</li>

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

11 </ol><h2>GCF of 75 and 100 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 75 and 100 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 75 = 1, 3, 5, 15, 25, 75.</p>

15 <p>Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 75 and 100: 1, 5, 25.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 25. The GCF of 75 and 100 is 25.</p>

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20 <h2>GCF of 75 and 100 Using Prime Factorization</h2>

19 <h2>GCF of 75 and 100 Using Prime Factorization</h2>

21 <p>To find the GCF of 75 and 100 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 75 and 100 using the Prime Factorization Method, follow these steps:</p>

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

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

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

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

24 <p>Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²</p>

23 <p>Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 5 x 5 = 5²</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 5 x 5 = 5²</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 5² = 25. The Greatest Common Factor of 75 and 100 is 25.</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 5² = 25. The Greatest Common Factor of 75 and 100 is 25.</p>

27 <h2>GCF of 75 and 100 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 75 and 100 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 75 and 100 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 75 and 100 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 Here, divide 100 by 75 100 ÷ 75 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 100 - (75×1) = 25 The remainder is 25, not zero, so continue the process</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 100 by 75 100 ÷ 75 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 100 - (75×1) = 25 The remainder is 25, not zero, so continue the process</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (75) by the previous remainder (25) Divide 75 by 25 75 ÷ 25 = 3 (quotient), remainder = 75 - (25×3) = 0</p>

29 <p><strong>Step 2:</strong>Now divide the previous divisor (75) by the previous remainder (25) Divide 75 by 25 75 ÷ 25 = 3 (quotient), remainder = 75 - (25×3) = 0</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 75 and 100 is 25.</p>

30 <p>The remainder is zero, the divisor will become the GCF. The GCF of 75 and 100 is 25.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 75 and 100</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 75 and 100</h2>

33 <p>Finding GCF of 75 and 100 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

32 <p>Finding GCF of 75 and 100 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>A florist has 75 roses and 100 tulips. She wants to create floral arrangements with the largest number of flowers in each without mixing types. How many flowers will be in each arrangement?</p>

34 <p>A florist has 75 roses and 100 tulips. She wants to create floral arrangements with the largest number of flowers in each without mixing types. How many flowers will be in each arrangement?</p>

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

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

37 <p>We should find the GCF of 75 and 100 GCF of 75 and 100 5² = 25.</p>

36 <p>We should find the GCF of 75 and 100 GCF of 75 and 100 5² = 25.</p>

38 <p>There are 25 flowers in each arrangement. 75 ÷ 25 = 3 100 ÷ 25 = 4</p>

37 <p>There are 25 flowers in each arrangement. 75 ÷ 25 = 3 100 ÷ 25 = 4</p>

39 <p>There will be 3 arrangements with roses and 4 arrangements with tulips, each containing 25 flowers.</p>

38 <p>There will be 3 arrangements with roses and 4 arrangements with tulips, each containing 25 flowers.</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>As the GCF of 75 and 100 is 25, the florist can make 25-flower arrangements. Now divide 75 and 100 by 25. Each arrangement has 3 sets of roses and 4 sets of tulips.</p>

40 <p>As the GCF of 75 and 100 is 25, the florist can make 25-flower arrangements. Now divide 75 and 100 by 25. Each arrangement has 3 sets of roses and 4 sets of tulips.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>A coach has 75 red jerseys and 100 blue jerseys. They want to distribute them in sets with an equal number of jerseys, using the largest possible number of jerseys per set. How many jerseys will be in each set?</p>

43 <p>A coach has 75 red jerseys and 100 blue jerseys. They want to distribute them in sets with an equal number of jerseys, using the largest possible number of jerseys per set. How many jerseys will be in each set?</p>

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

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

46 <p>GCF of 75 and 100 5² = 25.</p>

45 <p>GCF of 75 and 100 5² = 25.</p>

47 <p>So each set will have 25 jerseys.</p>

46 <p>So each set will have 25 jerseys.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 75 red and 100 blue jerseys. To find the total number of jerseys in each set, we should find the GCF of 75 and 100. There will be 25 jerseys in each set.</p>

48 <p>There are 75 red and 100 blue jerseys. To find the total number of jerseys in each set, we should find the GCF of 75 and 100. There will be 25 jerseys in each set.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>A tailor has 75 meters of red fabric and 100 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>

51 <p>A tailor has 75 meters of red fabric and 100 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>

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

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

54 <p>For calculating the longest equal length, we have to calculate the GCF of 75 and 100 The GCF of 75 and 100</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 75 and 100 The GCF of 75 and 100</p>

55 <p>5² = 25.</p>

54 <p>5² = 25.</p>

56 <p>The fabric is 25 meters long.</p>

55 <p>The fabric is 25 meters long.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 100 which is 25. The length of each piece of the fabric will be 25 meters.</p>

57 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 100 which is 25. The length of each piece of the fabric will be 25 meters.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

59 <h3>Problem 4</h3>

61 <p>A carpenter has two wooden planks, one 75 cm long and the other 100 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>

60 <p>A carpenter has two wooden planks, one 75 cm long and the other 100 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>

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

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

63 <p>The carpenter needs the longest piece of wood GCF of 75 and 100: 5² = 25.</p>

62 <p>The carpenter needs the longest piece of wood GCF of 75 and 100: 5² = 25.</p>

64 <p>The longest length of each piece is 25 cm.</p>

63 <p>The longest length of each piece is 25 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 100 cm, respectively. We have to find the GCF of 75 and 100, which is 25 cm. The longest length of each piece is 25 cm.</p>

65 <p>To find the longest length of each piece of the two wooden planks, 75 cm and 100 cm, respectively. We have to find the GCF of 75 and 100, which is 25 cm. The longest length of each piece is 25 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 ‘a’ is 25, and the LCM is 300. Find ‘a’.</p>

68 <p>If the GCF of 75 and ‘a’ is 25, and the LCM is 300. Find ‘a’.</p>

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

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

71 <p>The value of ‘a’ is 100.</p>

70 <p>The value of ‘a’ is 100.</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>25 × 300 = 75 × a</p>

73 <p>25 × 300 = 75 × a</p>

75 <p>7500 = 75a</p>

74 <p>7500 = 75a</p>

76 <p>a = 7500 ÷ 75 = 100</p>

75 <p>a = 7500 ÷ 75 = 100</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQs on the Greatest Common Factor of 75 and 100</h2>

77 <h2>FAQs on the Greatest Common Factor of 75 and 100</h2>

79 <h3>1.What is the LCM of 75 and 100?</h3>

78 <h3>1.What is the LCM of 75 and 100?</h3>

80 <p>The LCM of 75 and 100 is 300.</p>

79 <p>The LCM of 75 and 100 is 300.</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) is 12, which is divisible by 3.</p>

81 <p>Yes, 75 is divisible by 3 because the<a>sum</a>of its digits (7 + 5) is 12, which 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 100?</h3>

84 <h3>4.What is the prime factorization of 100?</h3>

86 <p>The prime factorization of 100 is 2² x 5².</p>

85 <p>The prime factorization of 100 is 2² x 5².</p>

87 <h3>5.Are 75 and 100 prime numbers?</h3>

86 <h3>5.Are 75 and 100 prime numbers?</h3>

88 <p>No, 75 and 100 are not prime numbers because both of them have more than two factors.</p>

87 <p>No, 75 and 100 are not prime numbers because both of them have more than two factors.</p>

89 <h2>Important Glossaries for GCF of 75 and 100</h2>

88 <h2>Important Glossaries for GCF of 75 and 100</h2>

90 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.</li>

89 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.</li>

91 </ul><ul><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>

90 </ul><ul><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>

92 </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 75 are 3 and 5.</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 75 are 3 and 5.</li>

93 </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>

92 </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>

94 </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 100 is 300.</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 100 is 300.</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>