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1 - <p>125 Learners</p>

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2 <p>Last updated on<strong>September 10, 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 25 and 40.</p>

4 <h2>What is the GCF of 25 and 40?</h2>

5 <p>The<a>greatest common factor</a>of 25 and 40 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. The GCF of two numbers cannot be negative because divisors are always positive.</p>

6 <h2>How to find the GCF of 25 and 40?</h2>

7 <p>To find the GCF of 25 and 40, 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 25 and 40 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 25 and 40 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 25 = 1, 5, 25.</p>

15 <p>Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 25 and 40: 1, 5.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 5. The GCF of 25 and 40 is 5.</p>

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20 <h2>GCF of 25 and 40 Using Prime Factorization</h2>

19 <h2>GCF of 25 and 40 Using Prime Factorization</h2>

21 <p>To find the GCF of 25 and 40 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 25 and 40 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 25: 25 = 5 × 5 = 5²</p>

22 <p>Prime Factors of 25: 25 = 5 × 5 = 5²</p>

24 <p>Prime Factors of 40: 40 = 2 × 2 × 2 × 5 = 2³ × 5</p>

23 <p>Prime Factors of 40: 40 = 2 × 2 × 2 × 5 = 2³ × 5</p>

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

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

26 <p><strong>Step 3:</strong>Multiply the common prime factors 5 = 5. The Greatest Common Factor of 25 and 40 is 5.</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 5 = 5. The Greatest Common Factor of 25 and 40 is 5.</p>

27 <h2>GCF of 25 and 40 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 25 and 40 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 25 and 40 using the Division Method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 25 and 40 using the Division 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 40 by 25 40 ÷ 25 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 40 - (25×1) = 15 The remainder is 15, not zero, so continue the process</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 40 by 25 40 ÷ 25 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 40 - (25×1) = 15 The remainder is 15, not zero, so continue the process</p>

30 <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>

29 <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 3:</strong>Divide the previous divisor (15) by the remainder (10) 15 ÷ 10 = 1 (quotient), remainder = 15 - (10×1) = 5</p>

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

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

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

33 <p>The remainder is zero, the divisor will become the GCF. The GCF of 25 and 40 is 5.</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 25 and 40 is 5.</p>

34 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 40</h2>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 40</h2>

35 <p>Finding the GCF of 25 and 40 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

34 <p>Finding the GCF of 25 and 40 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

36 <h3>Problem 1</h3>

35 <h3>Problem 1</h3>

37 <p>A farmer has 25 apple trees and 40 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?</p>

36 <p>A farmer has 25 apple trees and 40 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?</p>

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

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

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

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

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>As the GCF of 25 and 40 is 5, the farmer can make rows with 5 trees in each.</p>

40 <p>As the GCF of 25 and 40 is 5, the farmer can make rows with 5 trees in each.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>A chef has 25 kg of flour and 40 kg of sugar. He wants to pack them into bags with the same weight, using the largest possible weight per bag. What should be the weight of each bag?</p>

43 <p>A chef has 25 kg of flour and 40 kg of sugar. He wants to pack them into bags with the same weight, using the largest possible weight per bag. What should be the weight of each bag?</p>

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

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

46 <p>GCF of 25 and 40 5. So each bag will weigh 5 kg.</p>

45 <p>GCF of 25 and 40 5. So each bag will weigh 5 kg.</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>To pack the flour and sugar into bags of the same weight, we should find the GCF of 25 and 40. Each bag will weigh 5 kg.</p>

47 <p>To pack the flour and sugar into bags of the same weight, we should find the GCF of 25 and 40. Each bag will weigh 5 kg.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

49 <h3>Problem 3</h3>

51 <p>A library has 25 fiction books and 40 non-fiction books. The librarian wants to arrange them in sections with the same number of books in each section, using the largest possible number of books per section. How many books will be in each section?</p>

50 <p>A library has 25 fiction books and 40 non-fiction books. The librarian wants to arrange them in sections with the same number of books in each section, using the largest possible number of books per section. How many books will be in each section?</p>

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

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

53 <p>For calculating the largest number of books per section, we have to calculate the GCF of 25 and 40 The GCF of 25 and 40 5. Each section will have 5 books.</p>

52 <p>For calculating the largest number of books per section, we have to calculate the GCF of 25 and 40 The GCF of 25 and 40 5. Each section will have 5 books.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>For calculating the largest number of books per section, first, we need to calculate the GCF of 25 and 40, which is 5. Each section will have 5 books.</p>

54 <p>For calculating the largest number of books per section, first, we need to calculate the GCF of 25 and 40, which is 5. Each section will have 5 books.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

56 <h3>Problem 4</h3>

58 <p>A woodworker has two wooden planks, one 25 cm long and the other 40 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>

57 <p>A woodworker has two wooden planks, one 25 cm long and the other 40 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>

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

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

60 <p>The woodworker needs the longest piece of wood GCF of 25 and 40 5. The longest length of each piece is 5 cm.</p>

59 <p>The woodworker needs the longest piece of wood GCF of 25 and 40 5. The longest length of each piece is 5 cm.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>To find the longest length of each piece of the two wooden planks, 25 cm and 40 cm, respectively, we have to find the GCF of 25 and 40, which is 5 cm. The longest length of each piece is 5 cm.</p>

61 <p>To find the longest length of each piece of the two wooden planks, 25 cm and 40 cm, respectively, we have to find the GCF of 25 and 40, which is 5 cm. The longest length of each piece is 5 cm.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>If the GCF of 25 and ‘a’ is 5, and the LCM is 200, find ‘a’.</p>

64 <p>If the GCF of 25 and ‘a’ is 5, and the LCM is 200, find ‘a’.</p>

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

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

67 <p>The value of ‘a’ is 40.</p>

66 <p>The value of ‘a’ is 40.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>GCF × LCM = product of the numbers 5 × 200 = 25 × a 1000 = 25a a = 1000 ÷ 25 = 40</p>

68 <p>GCF × LCM = product of the numbers 5 × 200 = 25 × a 1000 = 25a a = 1000 ÷ 25 = 40</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQs on the Greatest Common Factor of 25 and 40</h2>

70 <h2>FAQs on the Greatest Common Factor of 25 and 40</h2>

72 <h3>1.What is the LCM of 25 and 40?</h3>

71 <h3>1.What is the LCM of 25 and 40?</h3>

73 <p>The LCM of 25 and 40 is 200.</p>

72 <p>The LCM of 25 and 40 is 200.</p>

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

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

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

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

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

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

77 <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>

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>

78 <h3>4.What is the prime factorization of 40?</h3>

77 <h3>4.What is the prime factorization of 40?</h3>

79 <p>The prime factorization of 40 is 2³ × 5.</p>

78 <p>The prime factorization of 40 is 2³ × 5.</p>

80 <h3>5.Are 25 and 40 prime numbers?</h3>

79 <h3>5.Are 25 and 40 prime numbers?</h3>

81 <p>No, 25 and 40 are not prime numbers because both of them have more than two factors.</p>

80 <p>No, 25 and 40 are not prime numbers because both of them have more than two factors.</p>

82 <h2>Important Glossaries for GCF of 25 and 40</h2>

81 <h2>Important Glossaries for GCF of 25 and 40</h2>

83 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

82 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

84 </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>

83 </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>

85 </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>

84 </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>

86 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.</li>

85 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.</li>

87 </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 40 is 200.</li>

86 </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 40 is 200.</li>

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

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

89 <p>▶</p>

88 <p>▶</p>

90 <h2>Hiralee Lalitkumar Makwana</h2>

89 <h2>Hiralee Lalitkumar Makwana</h2>

91 <h3>About the Author</h3>

90 <h3>About the Author</h3>

92 <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>

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>

93 <h3>Fun Fact</h3>

92 <h3>Fun Fact</h3>

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

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