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1 - <p>132 Learners</p>

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2 <p>Last updated on<strong>September 24, 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 28 and 40.</p>

4 <h2>What is the GCF of 28 and 40?</h2>

5 <p>The<a>greatest common factor</a>of 28 and 40 is 4.</p>

6 <p>The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers.</p>

7 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

8 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

9 <h2>How to find the GCF of 28 and 40?</h2>

10 <p>To find the GCF of 28 and 40, a few methods are described below -</p>

11 <p>Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm</p>

12 <h2>GCF of 28 and 40 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 28 and 40 using the listing of<a>factors</a></p>

14 <p>Step 1: Firstly, list the factors of each number Factors of 28 = 1, 2, 4, 7, 14, 28. Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40.</p>

15 <p>Step 2: Now, identify the<a>common factors</a>of them Common factors of 28 and 40: 1, 2, 4.</p>

16 <p>Step 3: Choose the largest factor The largest factor that both numbers have is 4.</p>

17 <p>The GCF of 28 and 40 is 4.</p>

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20 <h2>GCF of 28 and 40 Using Prime Factorization</h2>

19 <h2>GCF of 28 and 40 Using Prime Factorization</h2>

21 <p>To find the GCF of 28 and 40 using Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 28 and 40 using Prime Factorization Method, follow these steps:</p>

22 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 28: 28 = 2 x 2 x 7 = 2^2 x 7 Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2^3 x 5.</p>

21 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 28: 28 = 2 x 2 x 7 = 2^2 x 7 Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2^3 x 5.</p>

23 <p>Step 2: Now, identify the common prime factors The common prime factor is: 2 x 2 = 2^2 Step 3: Multiply the common prime factors 2^2 = 4.</p>

22 <p>Step 2: Now, identify the common prime factors The common prime factor is: 2 x 2 = 2^2 Step 3: Multiply the common prime factors 2^2 = 4.</p>

24 <p>The Greatest Common Factor of 28 and 40 is 4.</p>

23 <p>The Greatest Common Factor of 28 and 40 is 4.</p>

25 <h2>GCF of 28 and 40 Using Division Method or Euclidean Algorithm Method</h2>

24 <h2>GCF of 28 and 40 Using Division Method or Euclidean Algorithm Method</h2>

26 <p>Find the GCF of 28 and 40 using the<a>division</a>method or Euclidean Algorithm Method.</p>

25 <p>Find the GCF of 28 and 40 using the<a>division</a>method or Euclidean Algorithm Method.</p>

27 <p>Follow these steps:</p>

26 <p>Follow these steps:</p>

28 <p>Step 1: First, divide the larger number by the smaller number Here, divide 40 by 28 40 ÷ 28 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 40 - (28×1) = 12 The remainder is 12, not zero, so continue the process.</p>

27 <p>Step 1: First, divide the larger number by the smaller number Here, divide 40 by 28 40 ÷ 28 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 40 - (28×1) = 12 The remainder is 12, not zero, so continue the process.</p>

29 <p>Step 2: Now divide the previous divisor (28) by the previous remainder (12) Divide 28 by 12 28 ÷ 12 = 2 (quotient), remainder = 28 - (12×2) = 4.</p>

28 <p>Step 2: Now divide the previous divisor (28) by the previous remainder (12) Divide 28 by 12 28 ÷ 12 = 2 (quotient), remainder = 28 - (12×2) = 4.</p>

30 <p>Step 3: Now divide the previous divisor (12) by the previous remainder (4) 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0 The remainder is zero, the divisor will become the GCF.</p>

29 <p>Step 3: Now divide the previous divisor (12) by the previous remainder (4) 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0 The remainder is zero, the divisor will become the GCF.</p>

31 <p>The GCF of 28 and 40 is 4.</p>

30 <p>The GCF of 28 and 40 is 4.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 28 and 40</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 28 and 40</h2>

33 <p>Finding GCF of 28 and 40 looks simple, but students often make mistakes while calculating the GCF.</p>

32 <p>Finding GCF of 28 and 40 looks simple, but students often make mistakes while calculating the GCF.</p>

34 <p>Here are some common mistakes to be avoided by the students.</p>

33 <p>Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A gardener has 28 roses and 40 tulips. She wants to arrange them into bouquets with each bouquet having the same number of flowers. What is the largest number of flowers she can have in each bouquet?</p>

35 <p>A gardener has 28 roses and 40 tulips. She wants to arrange them into bouquets with each bouquet having the same number of flowers. What is the largest number of flowers she can have in each bouquet?</p>

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

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

38 <p>We should find the GCF of 28 and 40 GCF of 28 and 40 2^2 = 4.</p>

37 <p>We should find the GCF of 28 and 40 GCF of 28 and 40 2^2 = 4.</p>

39 <p>There are 4 flowers in each bouquet.</p>

38 <p>There are 4 flowers in each bouquet.</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>As the GCF of 28 and 40 is 4, the gardener can make bouquets with 4 flowers each.</p>

40 <p>As the GCF of 28 and 40 is 4, the gardener can make bouquets with 4 flowers each.</p>

42 <p>Divide 28 and 40 by 4 to know how many bouquets can be made.</p>

41 <p>Divide 28 and 40 by 4 to know how many bouquets can be made.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A coach has 28 soccer balls and 40 basketballs. He wants to group them into sets with the same number of balls, using the largest possible number of balls per set. How many balls will be in each set?</p>

44 <p>A coach has 28 soccer balls and 40 basketballs. He wants to group them into sets with the same number of balls, using the largest possible number of balls per set. How many balls will be in each set?</p>

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

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

47 <p>GCF of 28 and 40 2^2 = 4.</p>

46 <p>GCF of 28 and 40 2^2 = 4.</p>

48 <p>So each set will have 4 balls.</p>

47 <p>So each set will have 4 balls.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>There are 28 soccer balls and 40 basketballs.</p>

49 <p>There are 28 soccer balls and 40 basketballs.</p>

51 <p>To find the total number of balls in each set, we should find the GCF of 28 and 40.</p>

50 <p>To find the total number of balls in each set, we should find the GCF of 28 and 40.</p>

52 <p>There will be 4 balls in each set.</p>

51 <p>There will be 4 balls in each set.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

53 <h3>Problem 3</h3>

55 <p>A baker has 28 cups of flour and 40 cups of sugar. She wants to divide them into packs of equal size, using the largest possible size. What should be the size of each pack?</p>

54 <p>A baker has 28 cups of flour and 40 cups of sugar. She wants to divide them into packs of equal size, using the largest possible size. What should be the size of each pack?</p>

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

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

57 <p>For calculating the largest equal size, we have to calculate the GCF of 28 and 40, The GCF of 28 and 40 2^2 = 4.</p>

56 <p>For calculating the largest equal size, we have to calculate the GCF of 28 and 40, The GCF of 28 and 40 2^2 = 4.</p>

58 <p>Each pack will contain 4 cups of ingredients.</p>

57 <p>Each pack will contain 4 cups of ingredients.</p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>For calculating the largest size of each pack, we first need to calculate the GCF of 28 and 40, which is 4.</p>

59 <p>For calculating the largest size of each pack, we first need to calculate the GCF of 28 and 40, which is 4.</p>

61 <p>The size of each pack will be 4 cups.</p>

60 <p>The size of each pack will be 4 cups.</p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

62 <h3>Problem 4</h3>

64 <p>A tailor has 28 meters of blue fabric and 40 meters of red 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>

63 <p>A tailor has 28 meters of blue fabric and 40 meters of red 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>

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

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

66 <p>The tailor needs the longest piece of fabric GCF of 28 and 40 2^2 = 4.</p>

65 <p>The tailor needs the longest piece of fabric GCF of 28 and 40 2^2 = 4.</p>

67 <p>The longest length of each piece is 4 meters.</p>

66 <p>The longest length of each piece is 4 meters.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>To find the longest length of each piece of the two fabrics, 28 meters and 40 meters, respectively.</p>

68 <p>To find the longest length of each piece of the two fabrics, 28 meters and 40 meters, respectively.</p>

70 <p>We have to find the GCF of 28 and 40, which is 4 meters.</p>

69 <p>We have to find the GCF of 28 and 40, which is 4 meters.</p>

71 <p>The longest length of each piece is 4 meters.</p>

70 <p>The longest length of each piece is 4 meters.</p>

72 <p>Well explained 👍</p>

71 <p>Well explained 👍</p>

73 <h3>Problem 5</h3>

72 <h3>Problem 5</h3>

74 <p>If the GCF of 28 and ‘b’ is 4, and the LCM is 280. Find ‘b’.</p>

73 <p>If the GCF of 28 and ‘b’ is 4, and the LCM is 280. Find ‘b’.</p>

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

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

76 <p>The value of ‘b’ is 40.</p>

75 <p>The value of ‘b’ is 40.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>GCF x LCM = product of the numbers 4 × 280 = 28 × b 1120 = 28b b = 1120 ÷ 28 = 40</p>

77 <p>GCF x LCM = product of the numbers 4 × 280 = 28 × b 1120 = 28b b = 1120 ÷ 28 = 40</p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h2>FAQs on the Greatest Common Factor of 28 and 40</h2>

79 <h2>FAQs on the Greatest Common Factor of 28 and 40</h2>

81 <h3>1.What is the LCM of 28 and 40?</h3>

80 <h3>1.What is the LCM of 28 and 40?</h3>

82 <p>The LCM of 28 and 40 is 280.</p>

81 <p>The LCM of 28 and 40 is 280.</p>

83 <h3>2.Is 28 divisible by 2?</h3>

82 <h3>2.Is 28 divisible by 2?</h3>

84 <p>Yes, 28 is divisible by 2 because it is an even number.</p>

83 <p>Yes, 28 is divisible by 2 because it is an even number.</p>

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

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

86 <p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since</p>

85 <p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since</p>

87 <p>1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>

86 <p>1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>

88 <h3>4.What is the prime factorization of 40?</h3>

87 <h3>4.What is the prime factorization of 40?</h3>

89 <p>The prime factorization of 40 is 2^3 x 5.</p>

88 <p>The prime factorization of 40 is 2^3 x 5.</p>

90 <h3>5.Are 28 and 40 prime numbers?</h3>

89 <h3>5.Are 28 and 40 prime numbers?</h3>

91 <p>No, 28 and 40 are not prime numbers because both of them have more than two factors.</p>

90 <p>No, 28 and 40 are not prime numbers because both of them have more than two factors.</p>

92 <h2>Important Glossaries for GCF of 28 and 40</h2>

91 <h2>Important Glossaries for GCF of 28 and 40</h2>

93 <ul><li><strong>Factors</strong>: Factors are numbers that divide the target number completely. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.</li>

92 <ul><li><strong>Factors</strong>: Factors are numbers that divide the target number completely. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.</li>

94 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

93 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

95 </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 28 are 2 and 7.</li>

94 </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 28 are 2 and 7.</li>

96 </ul><ul><li><strong>Remainder</strong>: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.</li>

95 </ul><ul><li><strong>Remainder</strong>: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.</li>

97 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 28 and 40 is 280.</li>

96 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 28 and 40 is 280.</li>

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

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

99 <p>▶</p>

98 <p>▶</p>

100 <h2>Hiralee Lalitkumar Makwana</h2>

99 <h2>Hiralee Lalitkumar Makwana</h2>

101 <h3>About the Author</h3>

100 <h3>About the Author</h3>

102 <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>

101 <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>

103 <h3>Fun Fact</h3>

102 <h3>Fun Fact</h3>

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

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