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2 <p>Last updated on<strong>August 5, 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 16 and 81.</p>

4 <h2>What is the GCF of 16 and 81?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>16 and 81 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. 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>

6 <h2>How to find the GCF of 16 and 81?</h2>

7 <p>To find the GCF of 16 and 81, a few methods are described below:</p>

8 <ul><li>Listing Factors </li>

9 <li>Prime Factorization </li>

10 <li>Long Division Method / by Euclidean Algorithm</li>

11 </ul><h3>GCF of 16 and 81 by Using Listing of factors</h3>

12 <p>Steps to find the GCF of 16 and 81 using the listing of<a>factors</a>:</p>

13 <p><strong>Step 1:</strong>Firstly, list the factors of each number:</p>

14 <p>Factors of 16 = 1, 2, 4, 8, 16.</p>

15 <p>Factors of 81 = 1, 3, 9, 27, 81.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them, Common factor of 16 and 81: 1.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor</p>

18 <p>The largest factor that both numbers have is 1.</p>

19 <p>The GCF of 16 and 81 is 1.</p>

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22 <h3>GCF of 16 and 81 Using Prime Factorization</h3>

21 <h3>GCF of 16 and 81 Using Prime Factorization</h3>

23 <p>To find the GCF of 16 and 81 using Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 16 and 81 using Prime Factorization Method, follow these steps:</p>

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

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

25 <p>Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24</p>

24 <p>Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24</p>

26 <p>Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34</p>

25 <p>Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors. There are no common prime factors.</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors. There are no common prime factors.</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors Since there are no common prime factors, the GCF is 1.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors Since there are no common prime factors, the GCF is 1.</p>

29 <p>The Greatest Common Factor of 16 and 81 is 1.</p>

28 <p>The Greatest Common Factor of 16 and 81 is 1.</p>

30 <h3>GCF of 16 and 81 Using Division Method or Euclidean Algorithm Method</h3>

29 <h3>GCF of 16 and 81 Using Division Method or Euclidean Algorithm Method</h3>

31 <p>Find the GCF of 16 and 81 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 16 and 81 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

32 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

33 <p>Here, divide 81 by 16 81 ÷ 16 = 5 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (16×5) = 1</p>

32 <p>Here, divide 81 by 16 81 ÷ 16 = 5 (<a>quotient</a>), The<a>remainder</a>is calculated as 81 - (16×5) = 1</p>

34 <p>The remainder is 1, not zero, so continue the process</p>

33 <p>The remainder is 1, not zero, so continue the process</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1)</p>

34 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1)</p>

36 <p>Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 16 - (1×16) = 0</p>

35 <p>Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 16 - (1×16) = 0</p>

37 <p>The remainder is zero, the divisor will become the GCF.</p>

36 <p>The remainder is zero, the divisor will become the GCF.</p>

38 <p>The GCF of 16 and 81 is 1.</p>

37 <p>The GCF of 16 and 81 is 1.</p>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 81</h2>

38 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 81</h2>

40 <p>Finding GCF of 16 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>

39 <p>Finding GCF of 16 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>

41 <h3>Problem 1</h3>

40 <h3>Problem 1</h3>

42 <p>A chef has 16 apples and 81 oranges. She wants to create fruit baskets with all the fruits, using the largest possible equal number of fruits per basket. How many fruits will be in each basket?</p>

41 <p>A chef has 16 apples and 81 oranges. She wants to create fruit baskets with all the fruits, using the largest possible equal number of fruits per basket. How many fruits will be in each basket?</p>

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

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

44 <p>We should find GCF of 16 and 81 GCF of 16 and 81 is 1.</p>

43 <p>We should find GCF of 16 and 81 GCF of 16 and 81 is 1.</p>

45 <p>There will be 1 fruit per basket, as 16 and 81 have no other common factors.</p>

44 <p>There will be 1 fruit per basket, as 16 and 81 have no other common factors.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>As the GCF of 16 and 81 is 1, the chef can only put 1 fruit in each basket to have equal numbers of apples and oranges.</p>

46 <p>As the GCF of 16 and 81 is 1, the chef can only put 1 fruit in each basket to have equal numbers of apples and oranges.</p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 2</h3>

48 <h3>Problem 2</h3>

50 <p>A gardener has 16 rose plants and 81 tulip plants. They want to plant 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>

49 <p>A gardener has 16 rose plants and 81 tulip plants. They want to plant 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>

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

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

52 <p>GCF of 16 and 81 is 1. So each row will have 1 plant.</p>

51 <p>GCF of 16 and 81 is 1. So each row will have 1 plant.</p>

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 <p>There are 16 rose plants and 81 tulip plants. To find the total number of plants in each row, we should find the GCF of 16 and 81. There will be 1 plant in each row.</p>

53 <p>There are 16 rose plants and 81 tulip plants. To find the total number of plants in each row, we should find the GCF of 16 and 81. There will be 1 plant 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 16 meters of red cloth and 81 meters of blue cloth. She wants to cut both cloths into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

56 <p>A tailor has 16 meters of red cloth and 81 meters of blue cloth. She wants to cut both cloths 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 16 and 81 The GCF of 16 and 81 is 1. The length of each piece is 1 meter.</p>

58 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 81 The GCF of 16 and 81 is 1. The length of each piece is 1 meter.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>For calculating the longest length of the cloth first we need to calculate the GCF of 16 and 81 which is 1.</p>

60 <p>For calculating the longest length of the cloth first we need to calculate the GCF of 16 and 81 which is 1.</p>

62 <p>The length of each piece of the cloth will be 1 meter.</p>

61 <p>The length of each piece of the cloth will be 1 meter.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 4</h3>

63 <h3>Problem 4</h3>

65 <p>A carpenter has two wooden planks, one 16 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>

64 <p>A carpenter has two wooden planks, one 16 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>

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

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

67 <p>The carpenter needs the longest piece of wood</p>

66 <p>The carpenter needs the longest piece of wood</p>

68 <p>GCF of 16 and 81 is 1.</p>

67 <p>GCF of 16 and 81 is 1.</p>

69 <p>The longest length of each piece is 1 cm.</p>

68 <p>The longest length of each piece is 1 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, 16 cm and 81 cm, respectively.</p>

70 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 81 cm, respectively.</p>

72 <p>We have to find the GCF of 16 and 81, which is 1 cm.</p>

71 <p>We have to find the GCF of 16 and 81, which is 1 cm.</p>

73 <p>The longest length of each piece is 1 cm.</p>

72 <p>The longest length of each piece is 1 cm.</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h3>Problem 5</h3>

74 <h3>Problem 5</h3>

76 <p>If the GCF of 16 and ‘b’ is 1, and the LCM is 1296. Find ‘b’.</p>

75 <p>If the GCF of 16 and ‘b’ is 1, and the LCM is 1296. Find ‘b’.</p>

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

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

78 <p>The value of ‘b’ is 81.</p>

77 <p>The value of ‘b’ is 81.</p>

79 <h3>Explanation</h3>

78 <h3>Explanation</h3>

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

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

81 <p>1 × 1296 = 16 × b</p>

80 <p>1 × 1296 = 16 × b</p>

82 <p>1296 = 16b</p>

81 <p>1296 = 16b</p>

83 <p>b = 1296 ÷ 16 = 81</p>

82 <p>b = 1296 ÷ 16 = 81</p>

84 <p>Well explained 👍</p>

83 <p>Well explained 👍</p>

85 <h2>FAQs on the Greatest Common Factor of 16 and 81</h2>

84 <h2>FAQs on the Greatest Common Factor of 16 and 81</h2>

86 <h3>1.What is the LCM of 16 and 81?</h3>

85 <h3>1.What is the LCM of 16 and 81?</h3>

87 <p>The LCM of 16 and 81 is 1296.</p>

86 <p>The LCM of 16 and 81 is 1296.</p>

88 <h3>2.Is 16 divisible by 4?</h3>

87 <h3>2.Is 16 divisible by 4?</h3>

89 <p>Yes, 16 is divisible by 4 because 16 ÷ 4 = 4.</p>

88 <p>Yes, 16 is divisible by 4 because 16 ÷ 4 = 4.</p>

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

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

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

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

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

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

93 <h3>5.Are 16 and 81 prime numbers?</h3>

92 <h3>5.Are 16 and 81 prime numbers?</h3>

94 <p>No, 16 and 81 are not<a>prime numbers</a>because both of them have more than two factors.</p>

93 <p>No, 16 and 81 are not<a>prime numbers</a>because both of them have more than two factors.</p>

95 <h2>Important Glossaries for GCF of 16 and 81</h2>

94 <h2>Important Glossaries for GCF of 16 and 81</h2>

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

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

97 </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 81 are 3 x 3 x 3 x 3.</li>

96 </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 81 are 3 x 3 x 3 x 3.</li>

98 </ul><ul><li><strong>Co-prime Numbers:</strong>Two numbers that have no common factors other than 1. For example, 16 and 81 are co-prime.</li>

97 </ul><ul><li><strong>Co-prime Numbers:</strong>Two numbers that have no common factors other than 1. For example, 16 and 81 are co-prime.</li>

99 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 81 is divided by 16, the remainder is 1.</li>

98 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 81 is divided by 16, the remainder is 1.</li>

100 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 16 and 81 is 1296.</li>

99 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 16 and 81 is 1296.</li>

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

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

102 <p>▶</p>

101 <p>▶</p>

103 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h2>Hiralee Lalitkumar Makwana</h2>

104 <h3>About the Author</h3>

103 <h3>About the Author</h3>

105 <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 <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>

106 <h3>Fun Fact</h3>

105 <h3>Fun Fact</h3>

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

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