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1 - <p>127 Learners</p>

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2 <p>Last updated on<strong>October 25, 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 6 and 25.</p>

4 <h2>What is the GCF of 6 and 25?</h2>

5 <p>The<a>greatest common factor</a>of 6 and 25 is 1.</p>

6 <p>The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

7 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

8 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

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

10 <p>To find the GCF of 6 and 25, a few methods are described below -</p>

11 <p>Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

12 <h2>GCF of 6 and 25 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 6 and 25 using the listing of<a>factors</a></p>

14 <p>Step 1: Firstly, list the factors of each number Factors of 6 = 1, 2, 3, 6. Factors of 25 = 1, 5, 25.</p>

15 <p>Step 2: Now, identify the<a>common factors</a>of them Common factors of 6 and 25: 1.</p>

16 <p>Step 3: Choose the largest factor The largest factor that both numbers have is 1.</p>

17 <p>The GCF of 6 and 25 is 1.</p>

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20 <h2>GCF of 6 and 25 Using Prime Factorization</h2>

19 <h2>GCF of 6 and 25 Using Prime Factorization</h2>

21 <p>To find the GCF of 6 and 25 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 6 and 25 using the Prime Factorization Method, follow these steps:</p>

22 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 6: 6 = 2 x 3 Prime Factors of 25: 25 = 5 x 5.</p>

21 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 6: 6 = 2 x 3 Prime Factors of 25: 25 = 5 x 5.</p>

23 <p>Step 2: Now, identify the common prime factors There are no common prime factors.</p>

22 <p>Step 2: Now, identify the common prime factors There are no common prime factors.</p>

24 <p>Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.</p>

23 <p>Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.</p>

25 <p>The Greatest Common Factor of 6 and 25 is 1.</p>

24 <p>The Greatest Common Factor of 6 and 25 is 1.</p>

26 <h2>GCF of 6 and 25 Using Division Method or Euclidean Algorithm Method</h2>

25 <h2>GCF of 6 and 25 Using Division Method or Euclidean Algorithm Method</h2>

27 <p>Find the GCF of 6 and 25 using the<a>division</a>method or Euclidean Algorithm Method.</p>

26 <p>Find the GCF of 6 and 25 using the<a>division</a>method or Euclidean Algorithm Method.</p>

28 <p>Follow these steps:</p>

27 <p>Follow these steps:</p>

29 <p>Step 1: First, divide the larger number by the smaller number Here, divide 25 by 6 25 ÷ 6 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 25 - (6×4) = 1 The remainder is 1, not zero, so continue the process.</p>

28 <p>Step 1: First, divide the larger number by the smaller number Here, divide 25 by 6 25 ÷ 6 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 25 - (6×4) = 1 The remainder is 1, not zero, so continue the process.</p>

30 <p>Step 2: Now divide the previous divisor (6) by the previous remainder (1) Divide 6 by 1 6 ÷ 1 = 6 (quotient), remainder = 6 - (1×6) = 0 The remainder is zero, the divisor will become the GCF.</p>

29 <p>Step 2: Now divide the previous divisor (6) by the previous remainder (1) Divide 6 by 1 6 ÷ 1 = 6 (quotient), remainder = 6 - (1×6) = 0 The remainder is zero, the divisor will become the GCF.</p>

31 <p>The GCF of 6 and 25 is 1.</p>

30 <p>The GCF of 6 and 25 is 1.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 6 and 25</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 6 and 25</h2>

33 <p>Finding GCF of 6 and 25 looks simple, but students often make mistakes while calculating the GCF.</p>

32 <p>Finding GCF of 6 and 25 looks simple, but students often make mistakes while calculating the GCF.</p>

34 <p>Here are some common mistakes to be avoided by the students.</p>

33 <p>Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A gardener has 6 tulips and 25 roses. She wants to plant them in equal groups, with the largest number of flowers in each group. How many flowers will be in each group?</p>

35 <p>A gardener has 6 tulips and 25 roses. She wants to plant them in equal groups, with the largest number of flowers in each group. How many flowers will be in each group?</p>

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

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

38 <p>We should find the GCF of 6 and 25 GCF of 6 and 25 is 1.</p>

37 <p>We should find the GCF of 6 and 25 GCF of 6 and 25 is 1.</p>

39 <p>There are 1 equal group. 6 ÷ 1 = 6 25 ÷ 1 = 25.</p>

38 <p>There are 1 equal group. 6 ÷ 1 = 6 25 ÷ 1 = 25.</p>

40 <p>There will be 1 group, and each group gets 6 tulips and 25 roses.</p>

39 <p>There will be 1 group, and each group gets 6 tulips and 25 roses.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 6 and 25 is 1, the gardener can make 1 group. Now divide 6 and 25 by 1.</p>

41 <p>As the GCF of 6 and 25 is 1, the gardener can make 1 group. Now divide 6 and 25 by 1.</p>

43 <p>Each group gets 6 tulips and 25 roses.</p>

42 <p>Each group gets 6 tulips and 25 roses.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A school has 6 red markers and 25 blue markers. They want to distribute them equally among the students, using the largest possible number of markers per student. How many markers will each student receive?</p>

45 <p>A school has 6 red markers and 25 blue markers. They want to distribute them equally among the students, using the largest possible number of markers per student. How many markers will each student receive?</p>

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

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

48 <p>GCF of 6 and 25 is 1.</p>

47 <p>GCF of 6 and 25 is 1.</p>

49 <p>So each student will receive 1 marker.</p>

48 <p>So each student will receive 1 marker.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>There are 6 red and 25 blue markers.</p>

50 <p>There are 6 red and 25 blue markers.</p>

52 <p>To find the total number of markers each student receives, we should find the GCF of 6 and 25.</p>

51 <p>To find the total number of markers each student receives, we should find the GCF of 6 and 25.</p>

53 <p>Each student will receive 1 marker.</p>

52 <p>Each student will receive 1 marker.</p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

54 <h3>Problem 3</h3>

56 <p>A tailor has 6 meters of red fabric and 25 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>

55 <p>A tailor has 6 meters of red fabric and 25 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>

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

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

58 <p>For calculating the longest equal length, we have to calculate the GCF of 6 and 25.</p>

57 <p>For calculating the longest equal length, we have to calculate the GCF of 6 and 25.</p>

59 <p>The GCF of 6 and 25 is 1.</p>

58 <p>The GCF of 6 and 25 is 1.</p>

60 <p>The fabric is 1 meter long.</p>

59 <p>The fabric is 1 meter long.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 6 and 25 which is 1.</p>

61 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 6 and 25 which is 1.</p>

63 <p>The length of each piece of fabric will be 1 meter.</p>

62 <p>The length of each piece of fabric will be 1 meter.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

64 <h3>Problem 4</h3>

66 <p>A carpenter has two wooden planks, one 6 cm long and the other 25 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>

65 <p>A carpenter has two wooden planks, one 6 cm long and the other 25 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>

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

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

68 <p>The carpenter needs the longest piece of wood GCF of 6 and 25 is 1.</p>

67 <p>The carpenter needs the longest piece of wood GCF of 6 and 25 is 1.</p>

69 <p>The longest length of each piece is 1 cm.</p>

68 <p>The longest length of each piece is 1 cm.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>To find the longest length of each piece of the two wooden planks, 6 cm and 25 cm, respectively. We have to find the GCF of 6 and 25, which is 1 cm.</p>

70 <p>To find the longest length of each piece of the two wooden planks, 6 cm and 25 cm, respectively. We have to find the GCF of 6 and 25, which is 1 cm.</p>

72 <p>The longest length of each piece is 1 cm.</p>

71 <p>The longest length of each piece is 1 cm.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

73 <h3>Problem 5</h3>

75 <p>If the GCF of 6 and ‘b’ is 1, and the LCM is 150. Find ‘b’.</p>

74 <p>If the GCF of 6 and ‘b’ is 1, and the LCM is 150. Find ‘b’.</p>

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

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

77 <p>The value of ‘b’ is 25.</p>

76 <p>The value of ‘b’ is 25.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>GCF x LCM = product of the numbers 1 × 150 = 6 × b 150 = 6b b = 150 ÷ 6 = 25</p>

78 <p>GCF x LCM = product of the numbers 1 × 150 = 6 × b 150 = 6b b = 150 ÷ 6 = 25</p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h2>FAQs on the Greatest Common Factor of 6 and 25</h2>

80 <h2>FAQs on the Greatest Common Factor of 6 and 25</h2>

82 <h3>1.What is the LCM of 6 and 25?</h3>

81 <h3>1.What is the LCM of 6 and 25?</h3>

83 <p>The LCM of 6 and 25 is 150.</p>

82 <p>The LCM of 6 and 25 is 150.</p>

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

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

85 <p>Yes, 25 is divisible by 5 because it ends with a 5.</p>

84 <p>Yes, 25 is divisible by 5 because it ends with a 5.</p>

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

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

87 <p>The common factor of co-<a>prime numbers</a>is 1.</p>

86 <p>The common factor of co-<a>prime numbers</a>is 1.</p>

88 <p>Since 1 is the only common factor of any two co-prime numbers, it is said to be the GCF of any two co-prime numbers.</p>

87 <p>Since 1 is the only common factor of any two co-prime numbers, it is said to be the GCF of any two co-prime numbers.</p>

89 <h3>4.What is the prime factorization of 6?</h3>

88 <h3>4.What is the prime factorization of 6?</h3>

90 <p>The prime factorization of 6 is 2 x 3.</p>

89 <p>The prime factorization of 6 is 2 x 3.</p>

91 <h3>5.Are 6 and 25 prime numbers?</h3>

90 <h3>5.Are 6 and 25 prime numbers?</h3>

92 <p>No, 6 and 25 are not prime numbers because both of them have more than two factors.</p>

91 <p>No, 6 and 25 are not prime numbers because both of them have more than two factors.</p>

93 <h2>Important Glossaries for GCF of 6 and 25</h2>

92 <h2>Important Glossaries for GCF of 6 and 25</h2>

94 <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>

93 <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>

95 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

94 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

96 </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>

95 </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>

97 </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>

96 </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>

98 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 6 is 30.</li>

97 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 6 is 30.</li>

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

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

100 <p>▶</p>

99 <p>▶</p>

101 <h2>Hiralee Lalitkumar Makwana</h2>

100 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h3>About the Author</h3>

101 <h3>About the Author</h3>

103 <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>

102 <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>

104 <h3>Fun Fact</h3>

103 <h3>Fun Fact</h3>

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

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