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2 <p>Last updated on<strong>September 20, 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 to schedule events. In this topic, we will learn about the GCF of 25 and 14.</p>

4 <h2>What is the GCF of 25 and 14?</h2>

5 <p>The<a>greatest common factor</a>of 25 and 14 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. 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 14?</h2>

8 <p>To find the GCF of 25 and 14, a few methods are described below </p>

9 <ul><li>Listing Factors </li>

10 <li>Prime Factorization </li>

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

12 </ul><h2>GCF of 25 and 14 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 25 and 14 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 14 = 1, 2, 7, 14.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factor of 25 and 14: 1.</p>

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

19 <p>The GCF of 25 and 14 is 1.</p>

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22 <h2>GCF of 25 and 14 Using Prime Factorization</h2>

21 <h2>GCF of 25 and 14 Using Prime Factorization</h2>

23 <p>To find the GCF of 25 and 14 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 25 and 14 using the Prime Factorization Method, follow these steps:</p>

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

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

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

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

26 <p>Prime Factors of 14: 14 = 2 x 7</p>

25 <p>Prime Factors of 14: 14 = 2 x 7</p>

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

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

28 <p><strong>Step 3:</strong>The GCF is the<a>product</a>of the common prime factors Since there are no common prime factors, the GCF is 1.</p>

27 <p><strong>Step 3:</strong>The GCF is the<a>product</a>of the common prime factors Since there are no common prime factors, the GCF is 1.</p>

29 <p>The Greatest Common Factor of 25 and 14 is 1.</p>

28 <p>The Greatest Common Factor of 25 and 14 is 1.</p>

30 <h2>GCF of 25 and 14 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 25 and 14 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 25 and 14 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 25 and 14 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

32 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

33 <p>Here, divide 25 by 14 25 ÷ 14 = 1 (<a>quotient</a>),</p>

32 <p>Here, divide 25 by 14 25 ÷ 14 = 1 (<a>quotient</a>),</p>

34 <p>The<a>remainder</a>is calculated as 25 - (14×1) = 11</p>

33 <p>The<a>remainder</a>is calculated as 25 - (14×1) = 11</p>

35 <p>The remainder is 11, not zero, so continue the process</p>

34 <p>The remainder is 11, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (11)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (11)</p>

37 <p>Divide 14 by 11 14 ÷ 11 = 1 (quotient), remainder = 14 - (11×1) = 3</p>

36 <p>Divide 14 by 11 14 ÷ 11 = 1 (quotient), remainder = 14 - (11×1) = 3</p>

38 <p><strong>Step 3:</strong>Divide the previous divisor (11) by the new remainder (3) 11 ÷ 3 = 3 (quotient), remainder = 11 - (3×3) = 2</p>

37 <p><strong>Step 3:</strong>Divide the previous divisor (11) by the new remainder (3) 11 ÷ 3 = 3 (quotient), remainder = 11 - (3×3) = 2</p>

39 <p><strong>Step 4:</strong>Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1</p>

38 <p><strong>Step 4:</strong>Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1</p>

40 <p>Step 5: Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0</p>

39 <p>Step 5: Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0</p>

41 <p>The remainder is zero, so the divisor will become the GCF.</p>

40 <p>The remainder is zero, so the divisor will become the GCF.</p>

42 <p>The GCF of 25 and 14 is 1.</p>

41 <p>The GCF of 25 and 14 is 1.</p>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 14</h2>

42 <h2>Common Mistakes and How to Avoid Them in GCF of 25 and 14</h2>

44 <p>Finding the GCF of 25 and 14 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

43 <p>Finding the GCF of 25 and 14 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

45 <h3>Problem 1</h3>

44 <h3>Problem 1</h3>

46 <p>A teacher has 25 apples and 14 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

45 <p>A teacher has 25 apples and 14 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

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

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

48 <p>We should find the GCF of 25 and 14 The GCF of 25 and 14 is 1.</p>

47 <p>We should find the GCF of 25 and 14 The GCF of 25 and 14 is 1.</p>

49 <p>There are 1 equal groups 25 ÷ 1 = 25 14 ÷ 1 = 14</p>

48 <p>There are 1 equal groups 25 ÷ 1 = 25 14 ÷ 1 = 14</p>

50 <p>There will be 1 group, and each group gets 25 apples and 14 oranges.</p>

49 <p>There will be 1 group, and each group gets 25 apples and 14 oranges.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>As the GCF of 25 and 14 is 1, the teacher can make 1 group.</p>

51 <p>As the GCF of 25 and 14 is 1, the teacher can make 1 group.</p>

53 <p>Now divide 25 and 14 by 1.</p>

52 <p>Now divide 25 and 14 by 1.</p>

54 <p>Each group gets 25 apples and 14 oranges.</p>

53 <p>Each group gets 25 apples and 14 oranges.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 2</h3>

55 <h3>Problem 2</h3>

57 <p>A school has 25 red chairs and 14 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

56 <p>A school has 25 red chairs and 14 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

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

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

59 <p>The GCF of 25 and 14 is 1.</p>

58 <p>The GCF of 25 and 14 is 1.</p>

60 <p>So each row will have 1 chair.</p>

59 <p>So each row will have 1 chair.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>There are 25 red and 14 blue chairs.</p>

61 <p>There are 25 red and 14 blue chairs.</p>

63 <p>To find the total number of chairs in each row, we should find the GCF of 25 and 14.</p>

62 <p>To find the total number of chairs in each row, we should find the GCF of 25 and 14.</p>

64 <p>There will be 1 chair in each row.</p>

63 <p>There will be 1 chair in each row.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

65 <h3>Problem 3</h3>

67 <p>A tailor has 25 meters of red ribbon and 14 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

66 <p>A tailor has 25 meters of red ribbon and 14 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

69 <p>For calculating the longest equal length, we have to calculate the GCF of 25 and 14</p>

68 <p>For calculating the longest equal length, we have to calculate the GCF of 25 and 14</p>

70 <p>The GCF of 25 and 14 is 1.</p>

69 <p>The GCF of 25 and 14 is 1.</p>

71 <p>The ribbon is 1 meter long.</p>

70 <p>The ribbon is 1 meter long.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 25 and 14 which is 1.</p>

72 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 25 and 14 which is 1.</p>

74 <p>The length of each piece of the ribbon will be 1 meter.</p>

73 <p>The length of each piece of the ribbon will be 1 meter.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

75 <h3>Problem 4</h3>

77 <p>A carpenter has two wooden planks, one 25 cm long and the other 14 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>

76 <p>A carpenter has two wooden planks, one 25 cm long and the other 14 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>

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

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

79 <p>The carpenter needs the longest piece of wood</p>

78 <p>The carpenter needs the longest piece of wood</p>

80 <p>The GCF of 25 and 14 is 1.</p>

79 <p>The GCF of 25 and 14 is 1.</p>

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

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

82 <h3>Explanation</h3>

81 <h3>Explanation</h3>

83 <p>To find the longest length of each piece of the two wooden planks, 25 cm and 14 cm, respectively, we have to find the GCF of 25 and 14, which is 1 cm.</p>

82 <p>To find the longest length of each piece of the two wooden planks, 25 cm and 14 cm, respectively, we have to find the GCF of 25 and 14, which is 1 cm.</p>

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

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

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

85 <h3>Problem 5</h3>

87 <p>If the GCF of 25 and ‘a’ is 1, and the LCM is 350, find ‘a’.</p>

86 <p>If the GCF of 25 and ‘a’ is 1, and the LCM is 350, find ‘a’.</p>

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

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

89 <p>The value of ‘a’ is 14.</p>

88 <p>The value of ‘a’ is 14.</p>

90 <h3>Explanation</h3>

89 <h3>Explanation</h3>

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

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

92 <p>1 × 350 = 25 × a</p>

91 <p>1 × 350 = 25 × a</p>

93 <p>350 = 25a</p>

92 <p>350 = 25a</p>

94 <p>a = 350 ÷ 25 = 14</p>

93 <p>a = 350 ÷ 25 = 14</p>

95 <p>Well explained 👍</p>

94 <p>Well explained 👍</p>

96 <h2>FAQs on the Greatest Common Factor of 25 and 14</h2>

95 <h2>FAQs on the Greatest Common Factor of 25 and 14</h2>

97 <h3>1.What is the LCM of 25 and 14?</h3>

96 <h3>1.What is the LCM of 25 and 14?</h3>

98 <p>The LCM of 25 and 14 is 350.</p>

97 <p>The LCM of 25 and 14 is 350.</p>

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

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

100 <p>Yes, 25 is divisible by 5 because it is a multiple of 5.</p>

99 <p>Yes, 25 is divisible by 5 because it is a multiple of 5.</p>

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

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

102 <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>

101 <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>

103 <h3>4.What is the prime factorization of 14?</h3>

102 <h3>4.What is the prime factorization of 14?</h3>

104 <p>The prime factorization of 14 is 2 x 7.</p>

103 <p>The prime factorization of 14 is 2 x 7.</p>

105 <h3>5.Are 25 and 14 prime numbers?</h3>

104 <h3>5.Are 25 and 14 prime numbers?</h3>

106 <p>No, 25 and 14 are not prime numbers because both of them have more than two factors.</p>

105 <p>No, 25 and 14 are not prime numbers because both of them have more than two factors.</p>

107 <h2>Important Glossaries for GCF of 25 and 14</h2>

106 <h2>Important Glossaries for GCF of 25 and 14</h2>

108 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.</li>

107 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.</li>

109 </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>

108 </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>

110 </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 and 5.</li>

109 </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 and 5.</li>

111 </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 5, the remainder is 4 and the quotient is 2.</li>

110 </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 5, the remainder is 4 and the quotient is 2.</li>

112 </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 14 is 350.</li>

111 </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 14 is 350.</li>

113 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 25 and 14 is 1, as it is their largest common factor that divides the numbers completely.</li>

112 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 25 and 14 is 1, as it is their largest common factor that divides the numbers completely.</li>

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

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

115 <p>▶</p>

114 <p>▶</p>

116 <h2>Hiralee Lalitkumar Makwana</h2>

115 <h2>Hiralee Lalitkumar Makwana</h2>

117 <h3>About the Author</h3>

116 <h3>About the Author</h3>

118 <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>

117 <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>

119 <h3>Fun Fact</h3>

118 <h3>Fun Fact</h3>

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

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