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1 - <p>123 Learners</p>

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2 <p>Last updated on<strong>September 9, 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 24 and 84.</p>

4 <h2>What is the GCF of 24 and 84?</h2>

5 <p>The<a>greatest common factor</a>of 24 and 84 is 12. 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 24 and 84?</h2>

8 <p>To find the GCF of 24 and 84, 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 24 and 84 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 24 and 84 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 24 and 84: 1, 2, 3, 4, 6, 12.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 12. The GCF of 24 and 84 is 12.</p>

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19 <h2>GCF of 24 and 84 Using Prime Factorization</h2>

18 <h2>GCF of 24 and 84 Using Prime Factorization</h2>

20 <p>To find the GCF of 24 and 84 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 24 and 84 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 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3 Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3 Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2² × 3</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2² × 3</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors 2² × 3 = 4 × 3 = 12.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 2² × 3 = 4 × 3 = 12.</p>

24 <p>The Greatest Common Factor of 24 and 84 is 12.</p>

23 <p>The Greatest Common Factor of 24 and 84 is 12.</p>

25 <h2>GCF of 24 and 84 Using Division Method or Euclidean Algorithm Method</h2>

24 <h2>GCF of 24 and 84 Using Division Method or Euclidean Algorithm Method</h2>

26 <p>Find the GCF of 24 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

25 <p>Find the GCF of 24 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 24 84 ÷ 24 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (24 × 3) = 12 The remainder is 12, not zero, so continue the process</p>

26 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 24 84 ÷ 24 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (24 × 3) = 12 The remainder is 12, not zero, so continue the process</p>

28 <p><strong>Step 2:</strong>Now divide the previous divisor (24) by the previous remainder (12) Divide 24 by 12 24 ÷ 12 = 2 (quotient), remainder = 24 - (12 × 2) = 0 The remainder is zero, the divisor will become the GCF.</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (24) by the previous remainder (12) Divide 24 by 12 24 ÷ 12 = 2 (quotient), remainder = 24 - (12 × 2) = 0 The remainder is zero, the divisor will become the GCF.</p>

29 <p>The GCF of 24 and 84 is 12.</p>

28 <p>The GCF of 24 and 84 is 12.</p>

30 <h2>Common Mistakes and How to Avoid Them in GCF of 24 and 84</h2>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 24 and 84</h2>

31 <p>Finding GCF of 24 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>

30 <p>Finding GCF of 24 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>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>A gardener has 24 pots of red flowers and 84 pots of blue flowers. She wants to arrange them into groups with the largest number of pots in each group. How many pots will be in each group?</p>

32 <p>A gardener has 24 pots of red flowers and 84 pots of blue flowers. She wants to arrange them into groups with the largest number of pots in each group. How many pots will be in each group?</p>

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

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

35 <p>We should find the GCF of 24 and 84 GCF of 24 and 84 2² × 3 = 4 × 3 = 12. There are 12 equal groups 24 ÷ 12 = 2 84 ÷ 12 = 7 There will be 12 groups, and each group gets 2 pots of red flowers and 7 pots of blue flowers.</p>

34 <p>We should find the GCF of 24 and 84 GCF of 24 and 84 2² × 3 = 4 × 3 = 12. There are 12 equal groups 24 ÷ 12 = 2 84 ÷ 12 = 7 There will be 12 groups, and each group gets 2 pots of red flowers and 7 pots of blue flowers.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

37 <p>As the GCF of 24 and 84 is 12, the gardener can make 12 groups.</p>

36 <p>As the GCF of 24 and 84 is 12, the gardener can make 12 groups.</p>

38 <p>Now divide 24 and 84 by 12.</p>

37 <p>Now divide 24 and 84 by 12.</p>

39 <p>Each group gets 2 pots of red flowers and 7 pots of blue flowers.</p>

38 <p>Each group gets 2 pots of red flowers and 7 pots of blue flowers.</p>

40 <p>Well explained 👍</p>

39 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 <p>A decorator has 24 meters of red fabric and 84 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>

41 <p>A decorator has 24 meters of red fabric and 84 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>

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

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

44 <p>For calculating the longest equal length, we have to calculate the GCF of 24 and 84 The GCF of 24 and 84 2² × 3 = 4 × 3 = 12. The fabric is 12 meters long.</p>

43 <p>For calculating the longest equal length, we have to calculate the GCF of 24 and 84 The GCF of 24 and 84 2² × 3 = 4 × 3 = 12. The fabric is 12 meters long.</p>

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

46 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 24 and 84 which is 12.</p>

45 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 24 and 84 which is 12.</p>

47 <p>The length of each piece of fabric will be 12 meters.</p>

46 <p>The length of each piece of fabric will be 12 meters.</p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

48 <h3>Problem 3</h3>

50 <p>A chef has 24 pieces of chicken and 84 pieces of beef for a barbecue. He wants to create equal servings with the largest number of pieces in each serving. How many pieces will be in each serving?</p>

49 <p>A chef has 24 pieces of chicken and 84 pieces of beef for a barbecue. He wants to create equal servings with the largest number of pieces in each serving. How many pieces will be in each serving?</p>

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

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

52 <p>GCF of 24 and 84 2² × 3 = 4 × 3 = 12. Each serving will have 12 pieces.</p>

51 <p>GCF of 24 and 84 2² × 3 = 4 × 3 = 12. Each serving will have 12 pieces.</p>

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 <p>To find how many pieces will be in each serving, calculate the GCF of 24 and 84, which is 12.</p>

53 <p>To find how many pieces will be in each serving, calculate the GCF of 24 and 84, which is 12.</p>

55 <p>Each serving will include 12 pieces.</p>

54 <p>Each serving will include 12 pieces.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

56 <h3>Problem 4</h3>

58 <p>A teacher has 24 books on one topic and 84 books on another topic. She wants to organize them into the largest possible identical groups. How many books will be in each group?</p>

57 <p>A teacher has 24 books on one topic and 84 books on another topic. She wants to organize them into the largest possible identical groups. How many books will be in each group?</p>

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

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

60 <p>The teacher needs the largest group of books GCF of 24 and 84 2² × 3 = 4 × 3 = 12.</p>

59 <p>The teacher needs the largest group of books GCF of 24 and 84 2² × 3 = 4 × 3 = 12.</p>

61 <p>Each group will have 12 books.</p>

60 <p>Each group will have 12 books.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>To find the largest identical groups of books, we find the GCF of 24 and 84, which is 12.</p>

62 <p>To find the largest identical groups of books, we find the GCF of 24 and 84, which is 12.</p>

64 <p>There will be 12 books in each group.</p>

63 <p>There will be 12 books in each group.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

65 <h3>Problem 5</h3>

67 <p>If the GCF of 24 and ‘b’ is 12, and the LCM is 168. Find ‘b’.</p>

66 <p>If the GCF of 24 and ‘b’ is 12, and the LCM is 168. Find ‘b’.</p>

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

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

69 <p>The value of ‘b’ is 84.</p>

68 <p>The value of ‘b’ is 84.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

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

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

72 <p>12 × 168</p>

71 <p>12 × 168</p>

73 <p>= 24 × b</p>

72 <p>= 24 × b</p>

74 <p>2016 = 24b</p>

73 <p>2016 = 24b</p>

75 <p>b = 2016 ÷ 24 = 84</p>

74 <p>b = 2016 ÷ 24 = 84</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQs on the Greatest Common Factor of 24 and 84</h2>

76 <h2>FAQs on the Greatest Common Factor of 24 and 84</h2>

78 <h3>1.What is the LCM of 24 and 84?</h3>

77 <h3>1.What is the LCM of 24 and 84?</h3>

79 <p>The LCM of 24 and 84 is 168.</p>

78 <p>The LCM of 24 and 84 is 168.</p>

80 <h3>2.Is 84 divisible by 2?</h3>

79 <h3>2.Is 84 divisible by 2?</h3>

81 <p>Yes, 84 is divisible by 2 because it is an even number.</p>

80 <p>Yes, 84 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 84?</h3>

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

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

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

86 <h3>5.Are 24 and 84 prime numbers?</h3>

85 <h3>5.Are 24 and 84 prime numbers?</h3>

87 <p>No, 24 and 84 are not prime numbers because both of them have more than two factors.</p>

86 <p>No, 24 and 84 are not prime numbers because both of them have more than two factors.</p>

88 <h2>Important Glossaries for GCF of 24 and 84</h2>

87 <h2>Important Glossaries for GCF of 24 and 84</h2>

89 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>

88 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</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 4 are 4, 8, 12, 16, 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 4 are 4, 8, 12, 16, 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 15 are 3 and 5.</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 15 are 3 and 5.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

91 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</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 24 and 84 is 168.</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 24 and 84 is 168.</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>