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2 <p>Last updated on<strong>September 23, 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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 25 and 90.</p>

4 <h2>What is the GCF of 25 and 90?</h2>

5 <p>The<a>greatest common factor</a>of 25 and 90 is 5. 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.</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 25 and 90?</h2>

8 <p>To find the GCF of 25 and 90, 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 25 and 90 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 25 and 90 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 25 = 1, 5, 25.</p>

16 <p>Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 25 and 90: 1, 5.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 5. The GCF of 25 and 90 is 5.</p>

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21 <h2>GCF of 25 and 90 Using Prime Factorization</h2>

20 <h2>GCF of 25 and 90 Using Prime Factorization</h2>

22 <p>To find the GCF of 25 and 90 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 25 and 90 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 25: 25 = 5 x 5 = 5²</p>

23 <p>Prime Factors of 25: 25 = 5 x 5 = 5²</p>

25 <p>Prime Factors of 90: 90 = 2 x 3 x 3 x 5 = 2 x 3² x 5</p>

24 <p>Prime Factors of 90: 90 = 2 x 3 x 3 x 5 = 2 x 3² x 5</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 5.</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 5.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 25 and 90 is 5.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 25 and 90 is 5.</p>

28 <h2>GCF of 25 and 90 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 25 and 90 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 25 and 90 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 25 and 90 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 90 by 25 90 ÷ 25 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 90 - (25×3) = 15</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 90 by 25 90 ÷ 25 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 90 - (25×3) = 15</p>

31 <p>The remainder is 15, not zero, so continue the process</p>

30 <p>The remainder is 15, not zero, so continue the process</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (25) by the previous remainder (15) Divide 25 by 15 25 ÷ 15 = 1 (quotient), remainder = 25 - (15×1) = 10</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (25) by the previous remainder (15) Divide 25 by 15 25 ÷ 15 = 1 (quotient), remainder = 25 - (15×1) = 10</p>

33 <p><strong>Step 3:</strong>Divide the previous divisor (15) by the previous remainder (10) 15 ÷ 10 = 1 (quotient), remainder = 15 - (10×1) = 5</p>

32 <p><strong>Step 3:</strong>Divide the previous divisor (15) by the previous remainder (10) 15 ÷ 10 = 1 (quotient), remainder = 15 - (10×1) = 5</p>

34 <p><strong>Step 4:</strong>Divide the previous divisor (10) by the previous remainder (5) 10 ÷ 5 = 2 (quotient), remainder = 10 - (5×2) = 0</p>

33 <p><strong>Step 4:</strong>Divide the previous divisor (10) by the previous remainder (5) 10 ÷ 5 = 2 (quotient), remainder = 10 - (5×2) = 0</p>

35 <p>The remainder is zero, the divisor will become the GCF. The GCF of 25 and 90 is 5.</p>

34 <p>The remainder is zero, the divisor will become the GCF. The GCF of 25 and 90 is 5.</p>

36 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 90</h2>

35 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 90</h2>

37 <p>Finding the GCF of 25 and 90 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 the GCF of 25 and 90 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 25 tulips and 90 daffodils. She wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?</p>

38 <p>A gardener has 25 tulips and 90 daffodils. She wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per 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 the GCF of 25 and 90 GCF of 25 and 90 5. So each row will have 5 flowers.</p>

40 <p>We should find the GCF of 25 and 90 GCF of 25 and 90 5. So each row will have 5 flowers.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>As the GCF of 25 and 90 is 5, the gardener can plant 5 flowers in each row using the largest possible number.</p>

42 <p>As the GCF of 25 and 90 is 5, the gardener can plant 5 flowers in each row using the largest possible number.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A chef has 25 apples and 90 oranges. He wants to make baskets with equal numbers of fruits, using the largest number of fruits per basket. How many fruits will be in each basket?</p>

45 <p>A chef has 25 apples and 90 oranges. He wants to make baskets with equal numbers of fruits, using the largest number of fruits per basket. How many fruits will be in each basket?</p>

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

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

48 <p>GCF of 25 and 90 5. So each basket will have 5 fruits.</p>

47 <p>GCF of 25 and 90 5. So each basket will have 5 fruits.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>There are 25 apples and 90 oranges. To find the total number of fruits in each basket, we should find the GCF of 25 and 90. There will be 5 fruits in each basket.</p>

49 <p>There are 25 apples and 90 oranges. To find the total number of fruits in each basket, we should find the GCF of 25 and 90. There will be 5 fruits in each basket.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>A seamstress has 25 meters of cotton fabric and 90 meters of silk 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>

52 <p>A seamstress has 25 meters of cotton fabric and 90 meters of silk 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>

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

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

55 <p>For calculating the longest equal length, we have to calculate the GCF of 25 and 90.</p>

54 <p>For calculating the longest equal length, we have to calculate the GCF of 25 and 90.</p>

56 <p>The GCF of 25 and 90 is 5. The length of each piece is 5 meters.</p>

55 <p>The GCF of 25 and 90 is 5. The length of each piece is 5 meters.</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 25 and 90, which is 5. The length of each piece of fabric will be 5 meters.</p>

57 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 25 and 90, which is 5. The length of each piece of fabric will be 5 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 bricklayer has two slabs, one 25 cm long and the other 90 cm long. He wants to cut them into the longest possible equal pieces, without any material left over. What should be the length of each piece?</p>

60 <p>A bricklayer has two slabs, one 25 cm long and the other 90 cm long. He wants to cut them into the longest possible equal pieces, without any material 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 bricklayer needs the longest piece of material. GCF of 25 and 90 5.</p>

62 <p>The bricklayer needs the longest piece of material. GCF of 25 and 90 5.</p>

64 <p>The longest length of each piece is 5 cm.</p>

63 <p>The longest length of each piece is 5 cm.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the longest length of each piece of the two slabs, 25 cm and 90 cm respectively, we have to find the GCF of 25 and 90, which is 5 cm. The longest length of each piece is 5 cm.</p>

65 <p>To find the longest length of each piece of the two slabs, 25 cm and 90 cm respectively, we have to find the GCF of 25 and 90, which is 5 cm. The longest length of each piece is 5 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 25 and ‘b’ is 5, and the LCM is 450, find ‘b’.</p>

68 <p>If the GCF of 25 and ‘b’ is 5, and the LCM is 450, find ‘b’.</p>

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

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

71 <p>The value of ‘b’ is 90.</p>

70 <p>The value of ‘b’ is 90.</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>5 × 450 = 25 × b</p>

73 <p>5 × 450 = 25 × b</p>

75 <p>2250 = 25b</p>

74 <p>2250 = 25b</p>

76 <p>b = 2250 ÷ 25 = 90</p>

75 <p>b = 2250 ÷ 25 = 90</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQs on the Greatest Common Factor of 25 and 90</h2>

77 <h2>FAQs on the Greatest Common Factor of 25 and 90</h2>

79 <h3>1.What is the LCM of 25 and 90?</h3>

78 <h3>1.What is the LCM of 25 and 90?</h3>

80 <p>The LCM of 25 and 90 is 450.</p>

79 <p>The LCM of 25 and 90 is 450.</p>

81 <h3>2.Is 25 divisible by 5?</h3>

80 <h3>2.Is 25 divisible by 5?</h3>

82 <p>Yes, 25 is divisible by 5.</p>

81 <p>Yes, 25 is divisible by 5.</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 90?</h3>

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

86 <p>The prime factorization of 90 is 2 x 3² x 5.</p>

85 <p>The prime factorization of 90 is 2 x 3² x 5.</p>

87 <h3>5.Are 25 and 90 prime numbers?</h3>

86 <h3>5.Are 25 and 90 prime numbers?</h3>

88 <p>No, 25 and 90 are not prime numbers because both of them have more than two factors.</p>

87 <p>No, 25 and 90 are not prime numbers because both of them have more than two factors.</p>

89 <h2>Important Glossaries for GCF of 25 and 90</h2>

88 <h2>Important Glossaries for GCF of 25 and 90</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>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 25 are 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 25 are 5.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 6, the remainder is 1 and the quotient is 4.</li>

91 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 6, the remainder is 1 and the quotient is 4.</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 25 and 90 is 450.</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 25 and 90 is 450.</li>

94 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 25 and 90 is 5, 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 25 and 90 is 5, 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>