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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 schedule events. In this topic, we will learn about the GCF of 14 and 84.</p>

4 <h2>What is the GCF of 14 and 84?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>14 and 84 is 14. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers.</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 84?</h2>

8 <p>To find the GCF of 14 and 84, 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 84 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 14 and 84 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 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 14 and 84: 1, 2, 7, 14.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 14. The GCF of 14 and 84 is 14.</p>

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21 <h2>GCF of 14 and 84 Using Prime Factorization</h2>

20 <h2>GCF of 14 and 84 Using Prime Factorization</h2>

22 <p>To find the GCF of 14 and 84 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 14 and 84 using the Prime Factorization Method, follow these steps:</p>

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

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

24 <p>Prime Factors of 14: 14 = 2 × 7</p>

23 <p>Prime Factors of 14: 14 = 2 × 7</p>

25 <p>Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7</p>

24 <p>Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 7</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 7</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors The GCF is 2 × 7 = 14.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors The GCF is 2 × 7 = 14.</p>

28 <p>The Greatest Common Factor of 14 and 84 is 14.</p>

27 <p>The Greatest Common Factor of 14 and 84 is 14.</p>

29 <h2>GCF of 14 and 84 Using Division Method or Euclidean Algorithm Method</h2>

28 <h2>GCF of 14 and 84 Using Division Method or Euclidean Algorithm Method</h2>

30 <p>Find the GCF of 14 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

29 <p>Find the GCF of 14 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 14 84 ÷ 14 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (14×6) = 0</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 14 84 ÷ 14 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (14×6) = 0</p>

32 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 14 and 84 is 14.</p>

31 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 14 and 84 is 14.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 84</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 84</h2>

34 <p>Finding the GCF of 14 and 84 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 the GCF of 14 and 84 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 gardener has 14 roses and 84 tulips. She wants to arrange them into bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

35 <p>A gardener has 14 roses and 84 tulips. She wants to arrange them into bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

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

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

38 <p>We should find the GCF of 14 and 84 GCF of 14 and 84 is 14.</p>

37 <p>We should find the GCF of 14 and 84 GCF of 14 and 84 is 14.</p>

39 <p>There are 14 flowers in each bouquet. 14 ÷ 14 = 1 84 ÷ 14 = 6</p>

38 <p>There are 14 flowers in each bouquet. 14 ÷ 14 = 1 84 ÷ 14 = 6</p>

40 <p>There will be 7 bouquets, and each bouquet gets 1 rose and 6 tulips.</p>

39 <p>There will be 7 bouquets, and each bouquet gets 1 rose and 6 tulips.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 14 and 84 is 14, the gardener can make 7 bouquets. Now divide 14 and 84 by 14. Each bouquet gets 1 rose and 6 tulips.</p>

41 <p>As the GCF of 14 and 84 is 14, the gardener can make 7 bouquets. Now divide 14 and 84 by 14. Each bouquet gets 1 rose and 6 tulips.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A school has 14 small tables and 84 chairs. They want to arrange them in sets with the same number of tables and chairs in each set, using the largest possible number of items per set. How many items will be in each set?</p>

44 <p>A school has 14 small tables and 84 chairs. They want to arrange them in sets with the same number of tables and chairs in each set, using the largest possible number of items per set. How many items will be in each set?</p>

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

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

47 <p>GCF of 14 and 84 is 14. So each set will have 14 items.</p>

46 <p>GCF of 14 and 84 is 14. So each set will have 14 items.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 14 tables and 84 chairs. To find the total number of items in each set, we should find the GCF of 14 and 84. There will be 14 items in each set.</p>

48 <p>There are 14 tables and 84 chairs. To find the total number of items in each set, we should find the GCF of 14 and 84. There will be 14 items in each set.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>A chef has 14 kg of rice and 84 kg of wheat. She wants to pack them into bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?</p>

51 <p>A chef has 14 kg of rice and 84 kg of wheat. She wants to pack them into bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?</p>

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

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

54 <p>For calculating the largest equal weight, we have to calculate the GCF of 14 and 84. The GCF of 14 and 84 is 14. The weight of each bag is 14 kg.</p>

53 <p>For calculating the largest equal weight, we have to calculate the GCF of 14 and 84. The GCF of 14 and 84 is 14. The weight of each bag is 14 kg.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>For calculating the largest weight of the bags, we first need to calculate the GCF of 14 and 84, which is 14. The weight of each bag will be 14 kg.</p>

55 <p>For calculating the largest weight of the bags, we first need to calculate the GCF of 14 and 84, which is 14. The weight of each bag will be 14 kg.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

57 <h3>Problem 4</h3>

59 <p>A carpenter has two wooden planks, one 14 cm long and the other 84 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>

58 <p>A carpenter has two wooden planks, one 14 cm long and the other 84 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>

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

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

61 <p>The carpenter needs the longest piece of wood. GCF of 14 and 84 is 14. The longest length of each piece is 14 cm.</p>

60 <p>The carpenter needs the longest piece of wood. GCF of 14 and 84 is 14. The longest length of each piece is 14 cm.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>To find the longest length of each piece of the two wooden planks, 14 cm and 84 cm, respectively, we have to find the GCF of 14 and 84, which is 14 cm. The longest length of each piece is 14 cm.</p>

62 <p>To find the longest length of each piece of the two wooden planks, 14 cm and 84 cm, respectively, we have to find the GCF of 14 and 84, which is 14 cm. The longest length of each piece is 14 cm.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

64 <h3>Problem 5</h3>

66 <p>If the GCF of 14 and ‘b’ is 14, and the LCM is 168, find ‘b’.</p>

65 <p>If the GCF of 14 and ‘b’ is 14, and the LCM is 168, find ‘b’.</p>

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

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

68 <p>The value of ‘b’ is 84.</p>

67 <p>The value of ‘b’ is 84.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

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

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

71 <p>14 × 168 = 14 × b</p>

70 <p>14 × 168 = 14 × b</p>

72 <p>2352 = 14b</p>

71 <p>2352 = 14b</p>

73 <p>b = 2352 ÷ 14 = 168</p>

72 <p>b = 2352 ÷ 14 = 168</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQs on the Greatest Common Factor of 14 and 84</h2>

74 <h2>FAQs on the Greatest Common Factor of 14 and 84</h2>

76 <h3>1.What is the LCM of 14 and 84?</h3>

75 <h3>1.What is the LCM of 14 and 84?</h3>

77 <p>The LCM of 14 and 84 is 84.</p>

76 <p>The LCM of 14 and 84 is 84.</p>

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

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

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

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

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

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

81 <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>

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

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

83 <p>The prime factorization of 84 is 2² × 3 × 7.</p>

82 <p>The prime factorization of 84 is 2² × 3 × 7.</p>

84 <h3>5.Are 14 and 84 prime numbers?</h3>

83 <h3>5.Are 14 and 84 prime numbers?</h3>

85 <p>No, 14 and 84 are not prime numbers because both of them have more than two factors.</p>

84 <p>No, 14 and 84 are not prime numbers because both of them have more than two factors.</p>

86 <h2>Important Glossaries for GCF of 14 and 84</h2>

85 <h2>Important Glossaries for GCF of 14 and 84</h2>

87 <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>

86 <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><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>

87 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>

89 </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 14 are 2 and 7.</li>

88 </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 14 are 2 and 7.</li>

90 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 84 is divided by 14, the remainder is 0.</li>

89 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 84 is divided by 14, the remainder is 0.</li>

91 </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 84 is 84.</li>

90 </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 84 is 84.</li>

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Hiralee Lalitkumar Makwana</h2>

93 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h3>About the Author</h3>

94 <h3>About the Author</h3>

96 <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>

95 <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 <h3>Fun Fact</h3>

96 <h3>Fun Fact</h3>

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

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