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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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 14 and 35.</p>

4 <h2>What is the GCF of 14 and 35?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>14 and 35 is 7. 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 14 and 35?</h2>

8 <p>To find the GCF of 14 and 35, 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 14 and 35 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 14 and 35 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 14 = 1, 2, 7, 14.</p>

16 <p>Factors of 35 = 1, 5, 7, 35.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 14 and 35: 1, 7.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 7. The GCF of 14 and 35 is 7.</p>

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21 <h2>GCF of 14 and 35 Using Prime Factorization</h2>

20 <h2>GCF of 14 and 35 Using Prime Factorization</h2>

22 <p>To find the GCF of 14 and 35 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 14 and 35 using the Prime Factorization Method, follow these steps:</p>

23 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 14: 14 = 2 × 7 Prime Factors of 35: 35 = 5 × 7</p>

22 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 14: 14 = 2 × 7 Prime Factors of 35: 35 = 5 × 7</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 7</p>

23 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 7</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 7 = 7</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 7 = 7</p>

26 <p>The Greatest Common Factor of 14 and 35 is 7.</p>

25 <p>The Greatest Common Factor of 14 and 35 is 7.</p>

27 <h2>GCF of 14 and 35 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 14 and 35 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 14 and 35 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 14 and 35 using the<a>division</a>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 35 by 14 35 ÷ 14 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 35 - (14×2) = 7</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 35 by 14 35 ÷ 14 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 35 - (14×2) = 7</p>

30 <p>The remainder is 7, not zero, so continue the process</p>

29 <p>The remainder is 7, not zero, so continue the process</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 - (7×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 - (7×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

32 <p>The GCF of 14 and 35 is 7.</p>

31 <p>The GCF of 14 and 35 is 7.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 35</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 35</h2>

34 <p>Finding GCF of 14 and 35 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <p>Finding GCF of 14 and 35 looks simple, but students often make mistakes while calculating the GCF. 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 farmer has 14 apple trees and 35 orange trees. He wants to arrange them into equal rows with the largest possible number of trees in each row. How many trees will be in each row?</p>

35 <p>A farmer has 14 apple trees and 35 orange trees. He wants to arrange them into equal rows with the largest possible number of trees in each row. How many trees will be in each row?</p>

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

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

38 <p>We should find GCF of 14 and 35 GCF of 14 and 35 7</p>

37 <p>We should find GCF of 14 and 35 GCF of 14 and 35 7</p>

39 <p>There are 7 equal rows 14 ÷ 7 = 2 35 ÷ 7 = 5</p>

38 <p>There are 7 equal rows 14 ÷ 7 = 2 35 ÷ 7 = 5</p>

40 <p>There will be 7 rows, and each row gets 2 apple trees and 5 orange trees.</p>

39 <p>There will be 7 rows, and each row gets 2 apple trees and 5 orange trees.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 14 and 35 is 7, the farmer can make 7 rows. Now divide 14 and 35 by 7. Each row gets 2 apple trees and 5 orange trees.</p>

41 <p>As the GCF of 14 and 35 is 7, the farmer can make 7 rows. Now divide 14 and 35 by 7. Each row gets 2 apple trees and 5 orange trees.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A baker has 14 chocolate cupcakes and 35 vanilla cupcakes. She wants to pack them into boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?</p>

44 <p>A baker has 14 chocolate cupcakes and 35 vanilla cupcakes. She wants to pack them into boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?</p>

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

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

47 <p>GCF of 14 and 35 7 So each box will have 7 cupcakes.</p>

46 <p>GCF of 14 and 35 7 So each box will have 7 cupcakes.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 14 chocolate cupcakes and 35 vanilla cupcakes.</p>

48 <p>There are 14 chocolate cupcakes and 35 vanilla cupcakes.</p>

50 <p>To find the total number of cupcakes in each box, we should find the GCF of 14 and 35.</p>

49 <p>To find the total number of cupcakes in each box, we should find the GCF of 14 and 35.</p>

51 <p>There will be 7 cupcakes in each box.</p>

50 <p>There will be 7 cupcakes in each box.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

52 <h3>Problem 3</h3>

54 <p>A carpenter has 14 meters of pine wood and 35 meters of oak wood. He wants to cut both woods into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

53 <p>A carpenter has 14 meters of pine wood and 35 meters of oak wood. He wants to cut both woods into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

56 <p>For calculating the longest equal length, we have to calculate the GCF of 14 and 35 The GCF of 14 and 35 7 The length of each piece is 7 meters.</p>

55 <p>For calculating the longest equal length, we have to calculate the GCF of 14 and 35 The GCF of 14 and 35 7 The length of each piece is 7 meters.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>For calculating the longest length of the wood, first, we need to calculate the GCF of 14 and 35, which is 7. The length of each piece of wood will be 7 meters.</p>

57 <p>For calculating the longest length of the wood, first, we need to calculate the GCF of 14 and 35, which is 7. The length of each piece of wood will be 7 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 gardener has two types of flowers, 14 roses, and 35 tulips. He wants to plant them in groups with the largest possible number of flowers in each group, without any leftover flowers. How many flowers will be in each group?</p>

60 <p>A gardener has two types of flowers, 14 roses, and 35 tulips. He wants to plant them in groups with the largest possible number of flowers in each group, without any leftover flowers. How many flowers will be in each group?</p>

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

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

63 <p>The gardener needs the largest group of flowers GCF of 14 and 35 7 The largest number of flowers in each group is 7.</p>

62 <p>The gardener needs the largest group of flowers GCF of 14 and 35 7 The largest number of flowers in each group is 7.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>To find the largest number of flowers in each group of roses and tulips, 14 and 35, respectively, we have to find the GCF of 14 and 35, which is 7. The largest number of flowers in each group is 7.</p>

64 <p>To find the largest number of flowers in each group of roses and tulips, 14 and 35, respectively, we have to find the GCF of 14 and 35, which is 7. The largest number of flowers in each group is 7.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h3>Problem 5</h3>

66 <h3>Problem 5</h3>

68 <p>If the GCF of 14 and ‘b’ is 7, and the LCM is 70, find ‘b’.</p>

67 <p>If the GCF of 14 and ‘b’ is 7, and the LCM is 70, find ‘b’.</p>

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

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

70 <p>The value of ‘b’ is 35.</p>

69 <p>The value of ‘b’ is 35.</p>

71 <h3>Explanation</h3>

70 <h3>Explanation</h3>

72 <p>GCF × LCM = product of the numbers</p>

71 <p>GCF × LCM = product of the numbers</p>

73 <p>7 × 70 = 14 × b</p>

72 <p>7 × 70 = 14 × b</p>

74 <p>490 = 14b</p>

73 <p>490 = 14b</p>

75 <p>b = 490 ÷ 14 = 35</p>

74 <p>b = 490 ÷ 14 = 35</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQs on the Greatest Common Factor of 14 and 35</h2>

76 <h2>FAQs on the Greatest Common Factor of 14 and 35</h2>

78 <h3>1.What is the LCM of 14 and 35?</h3>

77 <h3>1.What is the LCM of 14 and 35?</h3>

79 <p>The LCM of 14 and 35 is 70.</p>

78 <p>The LCM of 14 and 35 is 70.</p>

80 <h3>2.Is 14 divisible by 2?</h3>

79 <h3>2.Is 14 divisible by 2?</h3>

81 <p>Yes, 14 is divisible by 2 because it is an even number.</p>

80 <p>Yes, 14 is divisible by 2 because it is an even number.</p>

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

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

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>

82 <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>

84 <h3>4.What is the prime factorization of 35?</h3>

83 <h3>4.What is the prime factorization of 35?</h3>

85 <p>The prime factorization of 35 is 5 × 7.</p>

84 <p>The prime factorization of 35 is 5 × 7.</p>

86 <h3>5.Are 14 and 35 prime numbers?</h3>

85 <h3>5.Are 14 and 35 prime numbers?</h3>

87 <p>No, 14 and 35 are not prime numbers because both of them have more than two factors.</p>

86 <p>No, 14 and 35 are not prime numbers because both of them have more than two factors.</p>

88 <h2>Important Glossaries for GCF of 14 and 35</h2>

87 <h2>Important Glossaries for GCF of 14 and 35</h2>

89 <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>

88 <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>

90 </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>

89 </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>

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 35 are 5 and 7.</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 35 are 5 and 7.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 35 is divided by 14, the remainder is 7.</li>

91 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 35 is divided by 14, the remainder is 7.</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 14 and 35 is 70.</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 14 and 35 is 70.</li>

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

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

95 <p>▶</p>

94 <p>▶</p>

96 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h3>About the Author</h3>

96 <h3>About the Author</h3>

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>

97 <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>

99 <h3>Fun Fact</h3>

98 <h3>Fun Fact</h3>

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

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