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1 - <p>139 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 16 and 28.</p>

4 <h2>What is the GCF of 16 and 28?</h2>

5 <p>The<a>greatest common factor</a>of 16 and 28 is 4. 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 28?</h2>

8 <p>To find the GCF of 16 and 28, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

9 <h2>GCF of 16 and 28 by Using Listing of factors</h2>

10 <p>Steps to find the GCF of 16 and 28 using the listing of<a>factors</a></p>

11 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16.</p>

12 <p>Factors of 28 = 1, 2, 4, 7, 14, 28.</p>

13 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 16 and 28: 1, 2, 4.</p>

14 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 4. The GCF of 16 and 28 is 4.</p>

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17 <h2>GCF of 16 and 28 Using Prime Factorization</h2>

16 <h2>GCF of 16 and 28 Using Prime Factorization</h2>

18 <p>To find the GCF of 16 and 28 using Prime Factorization Method, follow these steps:</p>

17 <p>To find the GCF of 16 and 28 using 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 16: 16 = 2 × 2 × 2 × 2 = 24</p>

18 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 24</p>

20 <p>Prime Factors of 28: 28 = 2 × 2 × 7 = 22 × 7</p>

19 <p>Prime Factors of 28: 28 = 2 × 2 × 7 = 22 × 7</p>

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

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

22 <p><strong>Step 3:</strong>Multiply the common prime factors 22 = 4.</p>

21 <p><strong>Step 3:</strong>Multiply the common prime factors 22 = 4.</p>

23 <p>The Greatest Common Factor of 16 and 28 is 4.</p>

22 <p>The Greatest Common Factor of 16 and 28 is 4.</p>

24 <h2>GCF of 16 and 28 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 16 and 28 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 16 and 28 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 16 and 28 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 28 by 16 28 ÷ 16 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 28 - (16×1) = 12 The remainder is 12, not zero, so continue the process</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 28 by 16 28 ÷ 16 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 28 - (16×1) = 12 The remainder is 12, not zero, so continue the process</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (12) Divide 16 by 12 16 ÷ 12 = 1 (quotient), remainder = 16 - (12×1) = 4</p>

26 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (12) Divide 16 by 12 16 ÷ 12 = 1 (quotient), remainder = 16 - (12×1) = 4</p>

28 <p>The remainder is 4, not zero, so continue the process</p>

27 <p>The remainder is 4, not zero, so continue the process</p>

29 <p><strong>Step 3:</strong>Now divide the previous divisor (12) by the previous remainder (4) Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0</p>

28 <p><strong>Step 3:</strong>Now divide the previous divisor (12) by the previous remainder (4) Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0</p>

30 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 28 is 4.</p>

29 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 28 is 4.</p>

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

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

32 <p>Finding GCF of 16 and 28 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

31 <p>Finding GCF of 16 and 28 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <h3>Problem 1</h3>

32 <h3>Problem 1</h3>

34 <p>A gardener has 16 red roses and 28 white roses. She wants to arrange them into equal bunches with the largest number of flowers in each bunch. How many flowers will be in each bunch?</p>

33 <p>A gardener has 16 red roses and 28 white roses. She wants to arrange them into equal bunches with the largest number of flowers in each bunch. How many flowers will be in each bunch?</p>

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

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

36 <p>We should find the GCF of 16 and 28 GCF of 16 and 28 2 × 2 = 4. There are 4 equal bunches 16 ÷ 4 = 4 28 ÷ 4 = 7 There will be 4 bunches, and each bunch gets 4 red roses and 7 white roses.</p>

35 <p>We should find the GCF of 16 and 28 GCF of 16 and 28 2 × 2 = 4. There are 4 equal bunches 16 ÷ 4 = 4 28 ÷ 4 = 7 There will be 4 bunches, and each bunch gets 4 red roses and 7 white roses.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>As the GCF of 16 and 28 is 4, the gardener can make 4 bunches. Now divide 16 and 28 by 4. Each bunch gets 4 red roses and 7 white roses.</p>

37 <p>As the GCF of 16 and 28 is 4, the gardener can make 4 bunches. Now divide 16 and 28 by 4. Each bunch gets 4 red roses and 7 white roses.</p>

39 <p>Well explained 👍</p>

38 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

39 <h3>Problem 2</h3>

41 <p>A construction company has 16 large bricks and 28 small bricks. They want to stack them in rows with the same number of bricks in each row, using the largest possible number of bricks per row. How many bricks will be in each row?</p>

40 <p>A construction company has 16 large bricks and 28 small bricks. They want to stack them in rows with the same number of bricks in each row, using the largest possible number of bricks per row. How many bricks will be in each row?</p>

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

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

43 <p>GCF of 16 and 28 2 × 2 = 4. So each row will have 4 bricks.</p>

42 <p>GCF of 16 and 28 2 × 2 = 4. So each row will have 4 bricks.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>There are 16 large and 28 small bricks. To find the total number of bricks in each row, we should find the GCF of 16 and 28. There will be 4 bricks in each row.</p>

44 <p>There are 16 large and 28 small bricks. To find the total number of bricks in each row, we should find the GCF of 16 and 28. There will be 4 bricks in each row.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>A chef has 16 tablespoons of sugar and 28 tablespoons of flour. She wants to divide both into portions of equal size, using the longest possible length. What should be the size of each portion?</p>

47 <p>A chef has 16 tablespoons of sugar and 28 tablespoons of flour. She wants to divide both into portions of equal size, using the longest possible length. What should be the size of each portion?</p>

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

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

50 <p>For calculating the longest equal size, we have to calculate the GCF of 16 and 28 The GCF of 16 and 28 2 × 2 = 4. The portion size is 4 tablespoons.</p>

49 <p>For calculating the longest equal size, we have to calculate the GCF of 16 and 28 The GCF of 16 and 28 2 × 2 = 4. The portion size is 4 tablespoons.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>For calculating the longest size of the portions first, we need to calculate the GCF of 16 and 28 which is 4. The size of each portion will be 4 tablespoons.</p>

51 <p>For calculating the longest size of the portions first, we need to calculate the GCF of 16 and 28 which is 4. The size of each portion will be 4 tablespoons.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>A designer has two pieces of fabric, one 16 meters long and the other 28 meters long. He wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?</p>

54 <p>A designer has two pieces of fabric, one 16 meters long and the other 28 meters long. He wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?</p>

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

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

57 <p>The designer needs the longest piece of fabric GCF of 16 and 28 2 × 2 = 4. The longest length of each piece is 4 meters.</p>

56 <p>The designer needs the longest piece of fabric GCF of 16 and 28 2 × 2 = 4. The longest length of each piece is 4 meters.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the longest length of each piece of the two pieces of fabric, 16 meters and 28 meters, respectively. We have to find the GCF of 16 and 28, which is 4 meters. The longest length of each piece is 4 meters.</p>

58 <p>To find the longest length of each piece of the two pieces of fabric, 16 meters and 28 meters, respectively. We have to find the GCF of 16 and 28, which is 4 meters. The longest length of each piece is 4 meters.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 5</h3>

60 <h3>Problem 5</h3>

62 <p>If the GCF of 16 and ‘b’ is 4, and the LCM is 112. Find ‘b’.</p>

61 <p>If the GCF of 16 and ‘b’ is 4, and the LCM is 112. Find ‘b’.</p>

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

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

64 <p>The value of ‘b’ is 28.</p>

63 <p>The value of ‘b’ is 28.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>GCF × LCM = product of the numbers 4 × 112 = 16 × b 448 = 16b b = 448 ÷ 16 = 28</p>

65 <p>GCF × LCM = product of the numbers 4 × 112 = 16 × b 448 = 16b b = 448 ÷ 16 = 28</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h2>FAQs on the Greatest Common Factor of 16 and 28</h2>

67 <h2>FAQs on the Greatest Common Factor of 16 and 28</h2>

69 <h3>1.What is the LCM of 16 and 28?</h3>

68 <h3>1.What is the LCM of 16 and 28?</h3>

70 <p>The LCM of 16 and 28 is 112.</p>

69 <p>The LCM of 16 and 28 is 112.</p>

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

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

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

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

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

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

74 <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>

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>

75 <h3>4.What is the prime factorization of 28?</h3>

74 <h3>4.What is the prime factorization of 28?</h3>

76 <p>The prime factorization of 28 is 2^2 × 7.</p>

75 <p>The prime factorization of 28 is 2^2 × 7.</p>

77 <h3>5.Are 16 and 28 prime numbers?</h3>

76 <h3>5.Are 16 and 28 prime numbers?</h3>

78 <p>No, 16 and 28 are not prime numbers because both of them have more than two factors.</p>

77 <p>No, 16 and 28 are not prime numbers because both of them have more than two factors.</p>

79 <h2>Important Glossaries for GCF of 16 and 28</h2>

78 <h2>Important Glossaries for GCF of 16 and 28</h2>

80 <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>

79 <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>

81 </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>

80 </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>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 18 are 2 and 3.</li>

81 </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 18 are 2 and 3.</li>

83 </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>

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 and the quotient is 3.</li>

84 </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 28 is 112.</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 16 and 28 is 112.</li>

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

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

86 <p>▶</p>

85 <p>▶</p>

87 <h2>Hiralee Lalitkumar Makwana</h2>

86 <h2>Hiralee Lalitkumar Makwana</h2>

88 <h3>About the Author</h3>

87 <h3>About the Author</h3>

89 <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>

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>

90 <h3>Fun Fact</h3>

89 <h3>Fun Fact</h3>

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

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