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1 - <p>210 Learners</p>

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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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 27 and 81.</p>

4 <h2>What is the GCF of 27 and 81?</h2>

5 <p>The<a>greatest common factor</a>of 27 and 81 is 27. 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 27 and 81?</h2>

8 <p>To find the GCF of 27 and 81, a few methods are described below: -</p>

9 <ol><li>Listing Factors </li>

10 <li>Prime Factorization </li>

11 <li>Long Division Method / Euclidean Algorithm</li>

12 </ol><h2>GCF of 27 and 81 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 27 and 81 using the listing of<a>factors</a>:</p>

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

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them. Common factors of 27 and 81: 1, 3, 9, 27.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor. The largest factor that both numbers have is 27. The GCF of 27 and 81 is 27.</p>

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19 <h2>GCF of 27 and 81 Using Prime Factorization</h2>

18 <h2>GCF of 27 and 81 Using Prime Factorization</h2>

20 <p>To find the GCF of 27 and 81 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 27 and 81 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 27: 27 = 3 x 3 x 3 = 3³ Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 3⁴</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number. Prime Factors of 27: 27 = 3 x 3 x 3 = 3³ Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 3⁴</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors. The common prime factors are: 3 x 3 x 3 = 3³</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors. The common prime factors are: 3 x 3 x 3 = 3³</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors. 3³ = 27. The Greatest Common Factor of 27 and 81 is 27.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors. 3³ = 27. The Greatest Common Factor of 27 and 81 is 27.</p>

24 <h2>GCF of 27 and 81 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 27 and 81 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 27 and 81 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 27 and 81 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 27. 81 ÷ 27 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (27×3) = 0.</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number. Here, divide 81 by 27. 81 ÷ 27 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (27×3) = 0.</p>

27 <p>Since the remainder is zero, the divisor will become the GCF. The GCF of 27 and 81 is 27.</p>

26 <p>Since the remainder is zero, the divisor will become the GCF. The GCF of 27 and 81 is 27.</p>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 27 and 81</h2>

27 <h2>Common Mistakes and How to Avoid Them in GCF of 27 and 81</h2>

29 <p>Finding the GCF of 27 and 81 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

28 <p>Finding the GCF of 27 and 81 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>A teacher has 27 notebooks and 81 pencils. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

30 <p>A teacher has 27 notebooks and 81 pencils. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

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

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

33 <p>We should find the GCF of 27 and 81. GCF of 27 and 81: 3³ = 27.</p>

32 <p>We should find the GCF of 27 and 81. GCF of 27 and 81: 3³ = 27.</p>

34 <p>There are 27 equal groups. 27 ÷ 27 = 1 81 ÷ 27 = 3</p>

33 <p>There are 27 equal groups. 27 ÷ 27 = 1 81 ÷ 27 = 3</p>

35 <p>There will be 27 groups, and each group gets 1 notebook and 3 pencils.</p>

34 <p>There will be 27 groups, and each group gets 1 notebook and 3 pencils.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

37 <p>As the GCF of 27 and 81 is 27, the teacher can make 27 groups. Now divide 27 and 81 by 27. Each group gets 1 notebook and 3 pencils.</p>

36 <p>As the GCF of 27 and 81 is 27, the teacher can make 27 groups. Now divide 27 and 81 by 27. Each group gets 1 notebook and 3 pencils.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>A school has 27 red flags and 81 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>A school has 27 red flags and 81 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 27 and 81: 3³ = 27. So each row will have 27 flags.</p>

41 <p>GCF of 27 and 81: 3³ = 27. So each row will have 27 flags.</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>There are 27 red and 81 blue flags. To find the total number of flags in each row, we should find the GCF of 27 and 81. There will be 27 flags in each row.</p>

43 <p>There are 27 red and 81 blue flags. To find the total number of flags in each row, we should find the GCF of 27 and 81. There will be 27 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 tailor has 27 meters of red fabric and 81 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>

46 <p>A tailor has 27 meters of red fabric and 81 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>

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 27 and 81. The GCF of 27 and 81: 3³ = 27. The fabric is 27 meters long.</p>

48 <p>For calculating the longest equal length, we have to calculate the GCF of 27 and 81. The GCF of 27 and 81: 3³ = 27. The fabric is 27 meters long.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 27 and 81, which is 27. The length of each piece of fabric will be 27 meters.</p>

50 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 27 and 81, which is 27. The length of each piece of fabric will be 27 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 27 cm long and the other 81 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 27 cm long and the other 81 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 27 and 81: 3³ = 27. The longest length of each piece is 27 cm.</p>

55 <p>The carpenter needs the longest piece of wood. GCF of 27 and 81: 3³ = 27. The longest length of each piece is 27 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, 27 cm and 81 cm, respectively, we have to find the GCF of 27 and 81, which is 27 cm. The longest length of each piece is 27 cm.</p>

57 <p>To find the longest length of each piece of the two wooden planks, 27 cm and 81 cm, respectively, we have to find the GCF of 27 and 81, which is 27 cm. The longest length of each piece is 27 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 27 and ‘a’ is 27, and the LCM is 81. Find ‘a’.</p>

60 <p>If the GCF of 27 and ‘a’ is 27, and the LCM is 81. Find ‘a’.</p>

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

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

63 <p>The value of ‘a’ is 81.</p>

62 <p>The value of ‘a’ is 81.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

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

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

66 <p>27 × 81 = 27 × a</p>

65 <p>27 × 81 = 27 × a</p>

67 <p>2187 = 27a</p>

66 <p>2187 = 27a</p>

68 <p>a = 2187 ÷ 27 = 81</p>

67 <p>a = 2187 ÷ 27 = 81</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQs on the Greatest Common Factor of 27 and 81</h2>

69 <h2>FAQs on the Greatest Common Factor of 27 and 81</h2>

71 <h3>1.What is the LCM of 27 and 81?</h3>

70 <h3>1.What is the LCM of 27 and 81?</h3>

72 <p>The LCM of 27 and 81 is 81.</p>

71 <p>The LCM of 27 and 81 is 81.</p>

73 <h3>2.Is 27 divisible by 3?</h3>

72 <h3>2.Is 27 divisible by 3?</h3>

74 <p>Yes, 27 is divisible by 3 because the<a>sum</a>of its digits (2 + 7 = 9) is divisible by 3.</p>

73 <p>Yes, 27 is divisible by 3 because the<a>sum</a>of its digits (2 + 7 = 9) is divisible by 3.</p>

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

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

76 <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>

75 <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>

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

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

78 <p>The prime factorization of 81 is 3⁴.</p>

77 <p>The prime factorization of 81 is 3⁴.</p>

79 <h3>5.Are 27 and 81 prime numbers?</h3>

78 <h3>5.Are 27 and 81 prime numbers?</h3>

80 <p>No, 27 and 81 are not prime numbers because both of them have more than two factors.</p>

79 <p>No, 27 and 81 are not prime numbers because both of them have more than two factors.</p>

81 <h2>Important Glossaries for GCF of 27 and 81</h2>

80 <h2>Important Glossaries for GCF of 27 and 81</h2>

82 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 27 are 1, 3, 9, and 27.</li>

81 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 27 are 1, 3, 9, and 27.</li>

83 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

82 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

84 </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 factor of 27 is 3.</li>

83 </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 factor of 27 is 3.</li>

85 </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, and the quotient is 3.</li>

84 </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, and the quotient is 3.</li>

86 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 27 and 81 is 81.</li>

85 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 27 and 81 is 81.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Hiralee Lalitkumar Makwana</h2>

88 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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>

90 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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