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2 <p>Last updated on<strong>September 23, 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 72 and 84.</p>

4 <h2>What is the GCF of 72 and 84?</h2>

5 <p>The<a>greatest common factor</a>of 72 and 84 is 12.</p>

6 <p>The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

7 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

8 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

9 <h2>How to find the GCF of 72 and 84?</h2>

10 <p>To find the GCF of 72 and 84, a few methods are described below -</p>

11 <p>Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

12 <h2>GCF of 72 and 84 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 72 and 84 using the listing of<a>factors</a></p>

14 <p>Step 1: Firstly, list the factors of each number Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>

15 <p>Step 2: Now, identify the<a>common factors</a>of them Common factors of 72 and 84: 1, 2, 3, 4, 6, 12.</p>

16 <p>Step 3: Choose the largest factor The largest factor that both numbers have is 12.</p>

17 <p>The GCF of 72 and 84 is 12.</p>

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20 <h2>GCF of 72 and 84 Using Prime Factorization</h2>

19 <h2>GCF of 72 and 84 Using Prime Factorization</h2>

21 <p>To find the GCF of 72 and 84 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 72 and 84 using the Prime Factorization Method, follow these steps:</p>

22 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2 Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2^2 x 3 x 7.</p>

21 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2 Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2^2 x 3 x 7.</p>

23 <p>Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 2^2 x 3.</p>

22 <p>Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 2^2 x 3.</p>

24 <p>Step 3: Multiply the common prime factors 2^2 x 3 = 4 × 3 = 12.</p>

23 <p>Step 3: Multiply the common prime factors 2^2 x 3 = 4 × 3 = 12.</p>

25 <p>The Greatest Common Factor of 72 and 84 is 12.</p>

24 <p>The Greatest Common Factor of 72 and 84 is 12.</p>

26 <h2>GCF of 72 and 84 Using Division Method or Euclidean Algorithm Method</h2>

25 <h2>GCF of 72 and 84 Using Division Method or Euclidean Algorithm Method</h2>

27 <p>Find the GCF of 72 and 84 using the<a>division</a>method or Euclidean Algorithm Method.</p>

26 <p>Find the GCF of 72 and 84 using the<a>division</a>method or Euclidean Algorithm Method.</p>

28 <p>Follow these steps:</p>

27 <p>Follow these steps:</p>

29 <p>Step 1: First, divide the larger number by the smaller number Here, divide 84 by 72 84 ÷ 72 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (72×1) = 12 The remainder is 12, not zero, so continue the process.</p>

28 <p>Step 1: First, divide the larger number by the smaller number Here, divide 84 by 72 84 ÷ 72 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 84 - (72×1) = 12 The remainder is 12, not zero, so continue the process.</p>

30 <p>Step 2: Now divide the previous divisor (72) by the previous remainder (12) Divide 72 by 12 72 ÷ 12 = 6 (quotient), remainder = 72 - (12×6) = 0 The remainder is zero, the divisor will become the GCF.</p>

29 <p>Step 2: Now divide the previous divisor (72) by the previous remainder (12) Divide 72 by 12 72 ÷ 12 = 6 (quotient), remainder = 72 - (12×6) = 0 The remainder is zero, the divisor will become the GCF.</p>

31 <p>The GCF of 72 and 84 is 12.</p>

30 <p>The GCF of 72 and 84 is 12.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 72 and 84</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 72 and 84</h2>

33 <p>Finding GCF of 72 and 84 looks simple, but students often make mistakes while calculating the GCF.</p>

32 <p>Finding GCF of 72 and 84 looks simple, but students often make mistakes while calculating the GCF.</p>

34 <p>Here are some common mistakes to be avoided by the students.</p>

33 <p>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 chef has 72 apples and 84 oranges. She wants to distribute them equally among her staff, with the largest possible number of fruits in each group. How many fruits will be in each group?</p>

35 <p>A chef has 72 apples and 84 oranges. She wants to distribute them equally among her staff, with the largest possible number of fruits in each group. How many fruits will be in each group?</p>

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

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

38 <p>We should find the GCF of 72 and 84 GCF of 72 and 84 2^2 x 3 = 4 x 3 = 12.</p>

37 <p>We should find the GCF of 72 and 84 GCF of 72 and 84 2^2 x 3 = 4 x 3 = 12.</p>

39 <p>There are 12 equal groups 72 ÷ 12 = 6 84 ÷ 12 = 7.</p>

38 <p>There are 12 equal groups 72 ÷ 12 = 6 84 ÷ 12 = 7.</p>

40 <p>There will be 12 groups, and each group gets 6 apples and 7 oranges.</p>

39 <p>There will be 12 groups, and each group gets 6 apples and 7 oranges.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 72 and 84 is 12, the chef can make 12 groups.</p>

41 <p>As the GCF of 72 and 84 is 12, the chef can make 12 groups.</p>

43 <p>Now divide 72 and 84 by 12. </p>

42 <p>Now divide 72 and 84 by 12. </p>

44 <p>Each group gets 6 apples and 7 oranges.</p>

43 <p>Each group gets 6 apples and 7 oranges.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>A gardener has 72 rose bushes and 84 tulip bulbs. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?</p>

46 <p>A gardener has 72 rose bushes and 84 tulip bulbs. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?</p>

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

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

49 <p>GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12. </p>

48 <p>GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12. </p>

50 <p>So each row will have 12 plants.</p>

49 <p>So each row will have 12 plants.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>There are 72 rose bushes and 84 tulip bulbs.</p>

51 <p>There are 72 rose bushes and 84 tulip bulbs.</p>

53 <p>To find the total number of plants in each row, we should find the GCF of 72 and 84.</p>

52 <p>To find the total number of plants in each row, we should find the GCF of 72 and 84.</p>

54 <p>There will be 12 plants in each row.</p>

53 <p>There will be 12 plants in each row.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 3</h3>

55 <h3>Problem 3</h3>

57 <p>A tailor has 72 meters of silk and 84 meters of cotton 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>

56 <p>A tailor has 72 meters of silk and 84 meters of cotton 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>

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

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

59 <p>For calculating the longest equal length, we have to calculate the GCF of 72 and 84 The GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12.</p>

58 <p>For calculating the longest equal length, we have to calculate the GCF of 72 and 84 The GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12.</p>

60 <p>The fabric is 12 meters long.</p>

59 <p>The fabric is 12 meters long.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 72 and 84, which is 12.</p>

61 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 72 and 84, which is 12.</p>

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

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

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

64 <h3>Problem 4</h3>

66 <p>A carpenter has two wooden planks, one 72 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>

65 <p>A carpenter has two wooden planks, one 72 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>

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

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

68 <p>The carpenter needs the longest piece of wood GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12.</p>

67 <p>The carpenter needs the longest piece of wood GCF of 72 and 84 2^2 x 3 = 4 × 3 = 12.</p>

69 <p>The longest length of each piece is 12 cm.</p>

68 <p>The longest length of each piece is 12 cm.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>To find the longest length of each piece of the two wooden planks, 72 cm and 84 cm, respectively, we have to find the GCF of 72 and 84, which is 12 cm.</p>

70 <p>To find the longest length of each piece of the two wooden planks, 72 cm and 84 cm, respectively, we have to find the GCF of 72 and 84, which is 12 cm.</p>

72 <p>The longest length of each piece is 12 cm.</p>

71 <p>The longest length of each piece is 12 cm.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

73 <h3>Problem 5</h3>

75 <p>If the GCF of 72 and ‘b’ is 12, and the LCM is 504. Find ‘b’.</p>

74 <p>If the GCF of 72 and ‘b’ is 12, and the LCM is 504. Find ‘b’.</p>

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

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

77 <p>The value of ‘b’ is 84.</p>

76 <p>The value of ‘b’ is 84.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>GCF x LCM = product of the numbers 12 × 504 = 72 × b 6048 = 72b b = 6048 ÷ 72 = 84</p>

78 <p>GCF x LCM = product of the numbers 12 × 504 = 72 × b 6048 = 72b b = 6048 ÷ 72 = 84</p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h2>FAQs on the Greatest Common Factor of 72 and 84</h2>

80 <h2>FAQs on the Greatest Common Factor of 72 and 84</h2>

82 <h3>1.What is the LCM of 72 and 84?</h3>

81 <h3>1.What is the LCM of 72 and 84?</h3>

83 <p>The LCM of 72 and 84 is 504.</p>

82 <p>The LCM of 72 and 84 is 504.</p>

84 <h3>2.Is 72 divisible by 2?</h3>

83 <h3>2.Is 72 divisible by 2?</h3>

85 <p>Yes, 72 is divisible by 2 because it is an even number.</p>

84 <p>Yes, 72 is divisible by 2 because it is an even number.</p>

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

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

87 <p>The common factor of<a>prime numbers</a>is 1 and the number itself.</p>

86 <p>The common factor of<a>prime numbers</a>is 1 and the number itself.</p>

88 <p>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>

87 <p>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>

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

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

90 <p>The prime factorization of 84 is 2^2 x 3 x 7.</p>

89 <p>The prime factorization of 84 is 2^2 x 3 x 7.</p>

91 <h3>5.Are 72 and 84 prime numbers?</h3>

90 <h3>5.Are 72 and 84 prime numbers?</h3>

92 <p>No, 72 and 84 are not prime numbers because both of them have more than two factors.</p>

91 <p>No, 72 and 84 are not prime numbers because both of them have more than two factors.</p>

93 <h2>Important Glossaries for GCF of 72 and 84</h2>

92 <h2>Important Glossaries for GCF of 72 and 84</h2>

94 <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>

93 <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>

95 </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>

94 </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>

96 </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>

95 </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>

97 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 72 and 84 is 504.</li>

96 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 72 and 84 is 504.</li>

98 </ul><ul><li><strong>GCF</strong>: The largest factor that commonly divides two or more numbers. For example, the GCF of 72 and 84 is 12, as it is their largest common factor that divides the numbers completely.</li>

97 </ul><ul><li><strong>GCF</strong>: The largest factor that commonly divides two or more numbers. For example, the GCF of 72 and 84 is 12, as it is their largest common factor that divides the numbers completely.</li>

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

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

100 <p>▶</p>

99 <p>▶</p>

101 <h2>Hiralee Lalitkumar Makwana</h2>

100 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h3>About the Author</h3>

101 <h3>About the Author</h3>

103 <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>

102 <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>

104 <h3>Fun Fact</h3>

103 <h3>Fun Fact</h3>

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

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