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2 <p>Last updated on<strong>August 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 26 and 65.</p>

4 <h2>What is the GCF of 26 and 65?</h2>

5 <p>The<a>greatest common factor</a>of 26 and 65 is 13. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>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>

7 <h2>How to find the GCF of 26 and 65?</h2>

8 <p>To find the GCF of 26 and 65, 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 26 and 65 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 26 and 65 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 26 = 1, 2, 13, 26. Factors of 65 = 1, 5, 13, 65.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 26 and 65: 1, 13.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 13. The GCF of 26 and 65 is 13.</p>

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19 <h2>GCF of 26 and 65 Using Prime Factorization</h2>

18 <h2>GCF of 26 and 65 Using Prime Factorization</h2>

20 <p>To find the GCF of 26 and 65 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 26 and 65 using the Prime Factorization Method, follow these steps:</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 26: 26 = 2 x 13 Prime Factors of 65: 65 = 5 x 13</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 26: 26 = 2 x 13 Prime Factors of 65: 65 = 5 x 13</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 13</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 13</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors 13 = 13. The Greatest Common Factor of 26 and 65 is 13.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 13 = 13. The Greatest Common Factor of 26 and 65 is 13.</p>

24 <h2>GCF of 26 and 65 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 26 and 65 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 26 and 65 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 26 and 65 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 65 by 26 65 ÷ 26 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 65 - (26×2) = 13 The remainder is 13, not zero, so continue the process</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 65 by 26 65 ÷ 26 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 65 - (26×2) = 13 The remainder is 13, not zero, so continue the process</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (26) by the previous remainder (13) Divide 26 by 13 26 ÷ 13 = 2 (quotient), remainder = 26 - (13×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

26 <p><strong>Step 2:</strong>Now divide the previous divisor (26) by the previous remainder (13) Divide 26 by 13 26 ÷ 13 = 2 (quotient), remainder = 26 - (13×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

28 <p>The GCF of 26 and 65 is 13.</p>

27 <p>The GCF of 26 and 65 is 13.</p>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 26 and 65</h2>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 26 and 65</h2>

30 <p>Finding GCF of 26 and 65 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

29 <p>Finding GCF of 26 and 65 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>A chef has 26 apples and 65 oranges. He wants to arrange them into the largest possible equal groups. How many fruits will be in each group?</p>

31 <p>A chef has 26 apples and 65 oranges. He wants to arrange them into the largest possible equal groups. How many fruits will be in each group?</p>

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

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

34 <p>We should find the GCF of 26 and 65 GCF of 26 and 65 is 13. There are 13 equal groups 26 ÷ 13 = 2 65 ÷ 13 = 5</p>

33 <p>We should find the GCF of 26 and 65 GCF of 26 and 65 is 13. There are 13 equal groups 26 ÷ 13 = 2 65 ÷ 13 = 5</p>

35 <p>There will be 13 groups, and each group gets 2 apples and 5 oranges.</p>

34 <p>There will be 13 groups, and each group gets 2 apples and 5 oranges.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

37 <p>As the GCF of 26 and 65 is 13, the chef can make 13 groups. Now divide 26 and 65 by 13. Each group gets 2 apples and 5 oranges.</p>

36 <p>As the GCF of 26 and 65 is 13, the chef can make 13 groups. Now divide 26 and 65 by 13. Each group gets 2 apples and 5 oranges.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>A school has 26 red flags and 65 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?</p>

39 <p>A school has 26 red flags and 65 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?</p>

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

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

42 <p>GCF of 26 and 65 is 13. So each row will have 13 flags.</p>

41 <p>GCF of 26 and 65 is 13. So each row will have 13 flags.</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>There are 26 red and 65 blue flags. To find the total number of flags in each row, we should find the GCF of 26 and 65. There will be 13 flags in each row.</p>

43 <p>There are 26 red and 65 blue flags. To find the total number of flags in each row, we should find the GCF of 26 and 65. There will be 13 flags in each row.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 3</h3>

45 <h3>Problem 3</h3>

47 <p>A tailor has 26 meters of red fabric and 65 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>

46 <p>A tailor has 26 meters of red fabric and 65 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>

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

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

49 <p>For calculating the longest equal length, we have to calculate the GCF of 26 and 65 The GCF of 26 and 65 is 13. The fabric is 13 meters long.</p>

48 <p>For calculating the longest equal length, we have to calculate the GCF of 26 and 65 The GCF of 26 and 65 is 13. The fabric is 13 meters long.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 26 and 65 which is 13.</p>

50 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 26 and 65 which is 13.</p>

52 <p>The length of each piece of the fabric will be 13 meters.</p>

51 <p>The length of each piece of the fabric will be 13 meters.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>A carpenter has two wooden planks, one 26 cm long and the other 65 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>

54 <p>A carpenter has two wooden planks, one 26 cm long and the other 65 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>

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

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

57 <p>The carpenter needs the longest piece of wood GCF of 26 and 65 is 13. The longest length of each piece is 13 cm.</p>

56 <p>The carpenter needs the longest piece of wood GCF of 26 and 65 is 13. The longest length of each piece is 13 cm.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the longest length of each piece of the two wooden planks, 26 cm and 65 cm, respectively, we have to find the GCF of 26 and 65, which is 13 cm. The longest length of each piece is 13 cm.</p>

58 <p>To find the longest length of each piece of the two wooden planks, 26 cm and 65 cm, respectively, we have to find the GCF of 26 and 65, which is 13 cm. The longest length of each piece is 13 cm.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 5</h3>

60 <h3>Problem 5</h3>

62 <p>If the GCF of 26 and ‘b’ is 13, and the LCM is 130. Find ‘b’.</p>

61 <p>If the GCF of 26 and ‘b’ is 13, and the LCM is 130. Find ‘b’.</p>

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

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

64 <p>The value of ‘b’ is 65.</p>

63 <p>The value of ‘b’ is 65.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

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

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

67 <p>13 × 130 = 26 × b</p>

66 <p>13 × 130 = 26 × b</p>

68 <p>1690 = 26b</p>

67 <p>1690 = 26b</p>

69 <p>b = 1690 ÷ 26 = 65</p>

68 <p>b = 1690 ÷ 26 = 65</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQs on the Greatest Common Factor of 26 and 65</h2>

70 <h2>FAQs on the Greatest Common Factor of 26 and 65</h2>

72 <h3>1.What is the LCM of 26 and 65?</h3>

71 <h3>1.What is the LCM of 26 and 65?</h3>

73 <p>The LCM of 26 and 65 is 130.</p>

72 <p>The LCM of 26 and 65 is 130.</p>

74 <h3>2.Is 26 divisible by 2?</h3>

73 <h3>2.Is 26 divisible by 2?</h3>

75 <p>Yes, 26 is divisible by 2 because it is an even number.</p>

74 <p>Yes, 26 is divisible by 2 because it is an even number.</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 65?</h3>

77 <h3>4.What is the prime factorization of 65?</h3>

79 <p>The prime factorization of 65 is 5 x 13.</p>

78 <p>The prime factorization of 65 is 5 x 13.</p>

80 <h3>5.Are 26 and 65 prime numbers?</h3>

79 <h3>5.Are 26 and 65 prime numbers?</h3>

81 <p>No, 26 and 65 are not prime numbers because both of them have more than two factors.</p>

80 <p>No, 26 and 65 are not prime numbers because both of them have more than two factors.</p>

82 <h2>Important Glossaries for GCF of 26 and 65</h2>

81 <h2>Important Glossaries for GCF of 26 and 65</h2>

83 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 13 are 1 and 13.</li>

82 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 13 are 1 and 13.</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 26 are 2 and 13.</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 26 are 2 and 13.</li>

86 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3.</li>

85 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3.</li>

87 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 26 and 65 is 13, as it is their largest common factor that divides the numbers completely.</li>

86 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 26 and 65 is 13, as it is their largest common factor that divides the numbers completely.</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>