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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 items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 16 and 72.</p>

4 <h2>What is the GCF of 16 and 72?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>16 and 72 is 8. 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 16 and 72?</h2>

8 <p>To find the GCF of 16 and 72, 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><h3>GCF of 16 and 72 by Using Listing of factors</h3>

13 <p>Steps to find the GCF of 16 and 72 using the listing of<a>factors</a>:</p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 16 and 72: 1, 2, 4, 8.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 8. The GCF of 16 and 72 is 8.</p>

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19 <h3>GCF of 16 and 72 Using Prime Factorization</h3>

18 <h3>GCF of 16 and 72 Using Prime Factorization</h3>

20 <p>To find the GCF of 16 and 72 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 16 and 72 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 16: 16 = 2 x 2 x 2 x 2 = 2⁴ Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2⁴ Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 2³</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 2³</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors 2³ = 8. The Greatest Common Factor of 16 and 72 is 8.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 2³ = 8. The Greatest Common Factor of 16 and 72 is 8.</p>

24 <h3>GCF of 16 and 72 Using Division Method or Euclidean Algorithm Method</h3>

23 <h3>GCF of 16 and 72 Using Division Method or Euclidean Algorithm Method</h3>

25 <p>Find the GCF of 16 and 72 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 16 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 72 by 16 72 ÷ 16 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 72 - (16×4) = 8 The remainder is 8, not zero, so continue the process</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 72 by 16 72 ÷ 16 = 4 (<a>quotient</a>), The<a>remainder</a>is calculated as 72 - (16×4) = 8 The remainder is 8, not zero, so continue the process</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (8) Divide 16 by 8 16 ÷ 8 = 2 (quotient), remainder = 16 - (8×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

26 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (8) Divide 16 by 8 16 ÷ 8 = 2 (quotient), remainder = 16 - (8×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

28 <p>The GCF of 16 and 72 is 8.</p>

27 <p>The GCF of 16 and 72 is 8.</p>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 72</h2>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 72</h2>

30 <p>Finding the GCF of 16 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>

29 <p>Finding the GCF of 16 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>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>A gardener has 16 rose bushes and 72 tulip bulbs. She wants to plant them in equal groups with the largest number of plants in each group. How many plants will be in each group?</p>

31 <p>A gardener has 16 rose bushes and 72 tulip bulbs. She wants to plant them in equal groups with the largest number of plants in each group. How many plants will be in each group?</p>

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

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

34 <p>We should find the GCF of 16 and 72 GCF of 16 and 72 2³ = 8. There are 8 equal groups 16 ÷ 8 = 2 72 ÷ 8 = 9 There will be 8 groups, and each group gets 2 rose bushes and 9 tulip bulbs.</p>

33 <p>We should find the GCF of 16 and 72 GCF of 16 and 72 2³ = 8. There are 8 equal groups 16 ÷ 8 = 2 72 ÷ 8 = 9 There will be 8 groups, and each group gets 2 rose bushes and 9 tulip bulbs.</p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

36 <p>As the GCF of 16 and 72 is 8, the gardener can make 8 groups.</p>

35 <p>As the GCF of 16 and 72 is 8, the gardener can make 8 groups.</p>

37 <p>Now divide 16 and 72 by 8.</p>

36 <p>Now divide 16 and 72 by 8.</p>

38 <p>Each group gets 2 rose bushes and 9 tulip bulbs.</p>

37 <p>Each group gets 2 rose bushes and 9 tulip bulbs.</p>

39 <p>Well explained 👍</p>

38 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

39 <h3>Problem 2</h3>

41 <p>A chef has 16 eggs and 72 slices of bread. He wants to create sandwiches with the same number of eggs and slices in each batch, using the maximum possible number of eggs per batch. How many eggs will be in each batch?</p>

40 <p>A chef has 16 eggs and 72 slices of bread. He wants to create sandwiches with the same number of eggs and slices in each batch, using the maximum possible number of eggs per batch. How many eggs will be in each batch?</p>

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

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

43 <p>GCF of 16 and 72 2³ = 8. So each batch will have 8 eggs.</p>

42 <p>GCF of 16 and 72 2³ = 8. So each batch will have 8 eggs.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>There are 16 eggs and 72 slices of bread.</p>

44 <p>There are 16 eggs and 72 slices of bread.</p>

46 <p>To find the total number of eggs in each batch, we should find the GCF of 16 and 72.</p>

45 <p>To find the total number of eggs in each batch, we should find the GCF of 16 and 72.</p>

47 <p>There will be 8 eggs in each batch.</p>

46 <p>There will be 8 eggs in each batch.</p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

48 <h3>Problem 3</h3>

50 <p>A farmer has 16 meters of fence and 72 square meters of field. She wants to split the field into sections with the longest possible equal perimeter. What should be the perimeter of each section?</p>

49 <p>A farmer has 16 meters of fence and 72 square meters of field. She wants to split the field into sections with the longest possible equal perimeter. What should be the perimeter of each section?</p>

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

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

52 <p>For calculating the longest equal perimeter, we have to calculate the GCF of 16 and 72 The GCF of 16 and 72 2³ = 8. The perimeter of each section is 8 meters.</p>

51 <p>For calculating the longest equal perimeter, we have to calculate the GCF of 16 and 72 The GCF of 16 and 72 2³ = 8. The perimeter of each section is 8 meters.</p>

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 <p>For calculating the longest perimeter of the sections, we first need to calculate the GCF of 16 and 72, which is 8.</p>

53 <p>For calculating the longest perimeter of the sections, we first need to calculate the GCF of 16 and 72, which is 8.</p>

55 <p>The perimeter of each section will be 8 meters.</p>

54 <p>The perimeter of each section will be 8 meters.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

56 <h3>Problem 4</h3>

58 <p>A carpenter has two wooden pieces, one 16 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>

57 <p>A carpenter has two wooden pieces, one 16 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>

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

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

60 <p>The carpenter needs the longest piece of wood GCF of 16 and 72 2³ = 8. The longest length of each piece is 8 cm.</p>

59 <p>The carpenter needs the longest piece of wood GCF of 16 and 72 2³ = 8. The longest length of each piece is 8 cm.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>To find the longest length of each piece of the two wooden pieces, 16 cm and 72 cm, respectively.</p>

61 <p>To find the longest length of each piece of the two wooden pieces, 16 cm and 72 cm, respectively.</p>

63 <p>We have to find the GCF of 16 and 72, which is 8 cm.</p>

62 <p>We have to find the GCF of 16 and 72, which is 8 cm.</p>

64 <p>The longest length of each piece is 8 cm.</p>

63 <p>The longest length of each piece is 8 cm.</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 16 and ‘b’ is 8, and the LCM is 144. Find ‘b’.</p>

66 <p>If the GCF of 16 and ‘b’ is 8, and the LCM is 144. Find ‘b’.</p>

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

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

69 <p>The value of ‘b’ is 72.</p>

68 <p>The value of ‘b’ is 72.</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>8 × 144</p>

71 <p>8 × 144</p>

73 <p>= 16 × b 1152</p>

72 <p>= 16 × b 1152</p>

74 <p>= 16b b</p>

73 <p>= 16b b</p>

75 <p>= 1152 ÷ 16 = 72</p>

74 <p>= 1152 ÷ 16 = 72</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQs on the Greatest Common Factor of 16 and 72</h2>

76 <h2>FAQs on the Greatest Common Factor of 16 and 72</h2>

78 <h3>1.What is the LCM of 16 and 72?</h3>

77 <h3>1.What is the LCM of 16 and 72?</h3>

79 <p>The LCM of 16 and 72 is 144.</p>

78 <p>The LCM of 16 and 72 is 144.</p>

80 <h3>2.Is 16 divisible by 2?</h3>

79 <h3>2.Is 16 divisible by 2?</h3>

81 <p>Yes, 16 is divisible by 2 because it is an even number.</p>

80 <p>Yes, 16 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 72?</h3>

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

85 <p>The prime factorization of 72 is 2³ x 3².</p>

84 <p>The prime factorization of 72 is 2³ x 3².</p>

86 <h3>5.Are 16 and 72 prime numbers?</h3>

85 <h3>5.Are 16 and 72 prime numbers?</h3>

87 <p>No, 16 and 72 are not prime numbers because both of them have more than two factors.</p>

86 <p>No, 16 and 72 are not prime numbers because both of them have more than two factors.</p>

88 <h2>Important Glossaries for GCF of 16 and 72</h2>

87 <h2>Important Glossaries for GCF of 16 and 72</h2>

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

88 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.</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 72 are 2 and 3.</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 72 are 2 and 3.</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 16 and 72 is 144.</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 16 and 72 is 144.</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>