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1 - <p>130 Learners</p>

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2 <p>Last updated on<strong>August 11, 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 81 and 72.</p>

4 <h2>What is the GCF of 81 and 72?</h2>

5 <p>The<a>greatest common factor</a>of 81 and 72 is 9. 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 81 and 72?</h2>

8 <p>To find the GCF of 81 and 72, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

9 <h2>GCF of 81 and 72 by Using Listing of factors</h2>

10 <p>Steps to find the GCF of 81 and 72 using the listing of<a>factors</a></p>

11 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 81 = 1, 3, 9, 27, 81.</p>

12 <p>Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.</p>

13 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 81 and 72: 1, 3, 9.</p>

14 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 9. The GCF of 81 and 72 is 9.</p>

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17 <h2>GCF of 81 and 72 Using Prime Factorization</h2>

16 <h2>GCF of 81 and 72 Using Prime Factorization</h2>

18 <p>To find the GCF of 81 and 72 using the Prime Factorization Method, follow these steps:</p>

17 <p>To find the GCF of 81 and 72 using the Prime Factorization Method, follow these steps:</p>

19 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34</p>

18 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34</p>

20 <p>Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32</p>

19 <p>Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 3 x 3 = 32</p>

20 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 3 x 3 = 32</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 32 = 3 x 3 = 9.</p>

21 <p><strong>Step 3:</strong>Multiply the common prime factors 32 = 3 x 3 = 9.</p>

23 <p>The Greatest Common Factor of 81 and 72 is 9.</p>

22 <p>The Greatest Common Factor of 81 and 72 is 9.</p>

24 <h2>GCF of 81 and 72 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 81 and 72 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 81 and 72 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 81 and 72 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 81 by 72 81 ÷ 72 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (72×1) = 9</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 81 by 72 81 ÷ 72 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (72×1) = 9</p>

27 <p>The remainder is 9, not zero, so continue the process</p>

26 <p>The remainder is 9, not zero, so continue the process</p>

28 <p><strong>Step 2:</strong>Now divide the previous divisor (72) by the previous remainder (9) Divide 72 by 9 72 ÷ 9 = 8 (quotient), remainder = 72 - (9×8) = 0</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (72) by the previous remainder (9) Divide 72 by 9 72 ÷ 9 = 8 (quotient), remainder = 72 - (9×8) = 0</p>

29 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 81 and 72 is 9.</p>

28 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 81 and 72 is 9.</p>

30 <h2>Common Mistakes and How to Avoid Them in GCF of 81 and 72</h2>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 81 and 72</h2>

31 <p>Finding the GCF of 81 and 72 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 the GCF of 81 and 72 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 chef has 81 apples and 72 oranges. She wants to make fruit baskets with an equal number of each fruit in each basket. What is the largest number of baskets she can make?</p>

32 <p>A chef has 81 apples and 72 oranges. She wants to make fruit baskets with an equal number of each fruit in each basket. What is the largest number of baskets she can make?</p>

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

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

35 <p>We should find the GCF of 81 and 72 GCF of 81 and 72 3^2 = 3 x 3 = 9. There are 9 equal baskets 81 ÷ 9 = 9 72 ÷ 9 = 8 There will be 9 baskets, and each basket gets 9 apples and 8 oranges.</p>

34 <p>We should find the GCF of 81 and 72 GCF of 81 and 72 3^2 = 3 x 3 = 9. There are 9 equal baskets 81 ÷ 9 = 9 72 ÷ 9 = 8 There will be 9 baskets, and each basket gets 9 apples and 8 oranges.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

37 <p>As the GCF of 81 and 72 is 9, the chef can make 9 baskets. Now divide 81 and 72 by 9. Each basket gets 9 apples and 8 oranges.</p>

36 <p>As the GCF of 81 and 72 is 9, the chef can make 9 baskets. Now divide 81 and 72 by 9. Each basket gets 9 apples and 8 oranges.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>An event organizer has 81 red flags and 72 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>An event organizer has 81 red flags and 72 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 81 and 72 3^2 = 3 x 3 = 9. So each row will have 9 flags.</p>

41 <p>GCF of 81 and 72 3^2 = 3 x 3 = 9. So each row will have 9 flags.</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>There are 81 red and 72 blue flags. To find the total number of flags in each row, we should find the GCF of 81 and 72. There will be 9 flags in each row.</p>

43 <p>There are 81 red and 72 blue flags. To find the total number of flags in each row, we should find the GCF of 81 and 72. There will be 9 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 gardener has 81 meters of red hose and 72 meters of blue hose. She wants to cut both hoses into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

46 <p>A gardener has 81 meters of red hose and 72 meters of blue hose. She wants to cut both hoses 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 81 and 72 The GCF of 81 and 72 3^2 = 3 x 3 = 9. The hose is 9 meters long.</p>

48 <p>For calculating the longest equal length, we have to calculate the GCF of 81 and 72 The GCF of 81 and 72 3^2 = 3 x 3 = 9. The hose is 9 meters long.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>For calculating the longest length of the hose first, we need to calculate the GCF of 81 and 72, which is 9. The length of each piece of the hose will be 9 meters.</p>

50 <p>For calculating the longest length of the hose first, we need to calculate the GCF of 81 and 72, which is 9. The length of each piece of the hose will be 9 meters.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 4</h3>

52 <h3>Problem 4</h3>

54 <p>A carpenter has two wooden planks, one 81 cm long and the other 72 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>

53 <p>A carpenter has two wooden planks, one 81 cm long and the other 72 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>

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

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

56 <p>The carpenter needs the longest piece of wood GCF of 81 and 72 3^2 = 3 x 3 = 9. The longest length of each piece is 9 cm.</p>

55 <p>The carpenter needs the longest piece of wood GCF of 81 and 72 3^2 = 3 x 3 = 9. The longest length of each piece is 9 cm.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>To find the longest length of each piece of the two wooden planks, 81 cm and 72 cm, respectively. We have to find the GCF of 81 and 72, which is 9 cm. The longest length of each piece is 9 cm.</p>

57 <p>To find the longest length of each piece of the two wooden planks, 81 cm and 72 cm, respectively. We have to find the GCF of 81 and 72, which is 9 cm. The longest length of each piece is 9 cm.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 5</h3>

59 <h3>Problem 5</h3>

61 <p>If the GCF of 81 and ‘a’ is 9, and the LCM is 648. Find ‘a’.</p>

60 <p>If the GCF of 81 and ‘a’ is 9, and the LCM is 648. Find ‘a’.</p>

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

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

63 <p>The value of ‘a’ is 72.</p>

62 <p>The value of ‘a’ is 72.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>GCF x LCM = product of the numbers 9 × 648 = 81 × a 5832 = 81a a = 5832 ÷ 81 = 72</p>

64 <p>GCF x LCM = product of the numbers 9 × 648 = 81 × a 5832 = 81a a = 5832 ÷ 81 = 72</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

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

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

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

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

69 <p>The LCM of 81 and 72 is 648.</p>

68 <p>The LCM of 81 and 72 is 648.</p>

70 <h3>2.Is 81 divisible by 3?</h3>

69 <h3>2.Is 81 divisible by 3?</h3>

71 <p>Yes, 81 is divisible by 3 because the<a>sum</a>of its digits (8+1) is 9, which is divisible by 3.</p>

70 <p>Yes, 81 is divisible by 3 because the<a>sum</a>of its digits (8+1) is 9, which is divisible by 3.</p>

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

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

73 <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>

72 <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>

74 <h3>4.What is the prime factorization of 72?</h3>

73 <h3>4.What is the prime factorization of 72?</h3>

75 <p>The prime factorization of 72 is 2^3 x 3^2.</p>

74 <p>The prime factorization of 72 is 2^3 x 3^2.</p>

76 <h3>5.Are 81 and 72 prime numbers?</h3>

75 <h3>5.Are 81 and 72 prime numbers?</h3>

77 <p>No, 81 and 72 are not prime numbers because both of them have more than two factors.</p>

76 <p>No, 81 and 72 are not prime numbers because both of them have more than two factors.</p>

78 <h2>Important Glossaries for GCF of 81 and 72</h2>

77 <h2>Important Glossaries for GCF of 81 and 72</h2>

79 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

78 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

80 </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 72 are 2 and 3.</li>

79 </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 72 are 2 and 3.</li>

81 </ul><ul><li><strong>Euclidean Algorithm:</strong>A method for finding the greatest common divisor of two numbers by dividing and replacing until the remainder is zero.</li>

80 </ul><ul><li><strong>Euclidean Algorithm:</strong>A method for finding the greatest common divisor of two numbers by dividing and replacing until the remainder is zero.</li>

82 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1.</li>

81 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1.</li>

83 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 81 and 72 is 648.</li>

82 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 81 and 72 is 648.</li>

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

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

85 <p>▶</p>

84 <p>▶</p>

86 <h2>Hiralee Lalitkumar Makwana</h2>

85 <h2>Hiralee Lalitkumar Makwana</h2>

87 <h3>About the Author</h3>

86 <h3>About the Author</h3>

88 <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>

87 <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>

89 <h3>Fun Fact</h3>

88 <h3>Fun Fact</h3>

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

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