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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 28 and 70.</p>

4 <h2>What is the GCF of 28 and 70?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>28 and 70 is 14. 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 28 and 70?</h2>

7 <p>To find the GCF of 28 and 70, a few methods are described below:</p>

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

9 </ul><ul><li>Prime Factorization</li>

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

11 </ul><h3>GCF of 28 and 70 by Using Listing of factors</h3>

12 <p>Steps to find the GCF of 28 and 70 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 28 = 1, 2, 4, 7, 14, 28.</p>

15 <p>Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them.</p>

17 <p>Common factors of 28 and 70: 1, 2, 7, 14.</p>

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

19 <p>The largest factor that both numbers have is 14.</p>

20 <p>The GCF of 28 and 70 is 14.</p>

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23 <h3>GCF of 28 and 70 Using Prime Factorization</h3>

22 <h3>GCF of 28 and 70 Using Prime Factorization</h3>

24 <p>To find the GCF of 28 and 70 using the Prime Factorization Method, follow these steps:</p>

23 <p>To find the GCF of 28 and 70 using the Prime Factorization Method, follow these steps:</p>

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

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

26 <p>Prime factors of 28: 28 = 2 x 2 x 7 = 22 x 7</p>

25 <p>Prime factors of 28: 28 = 2 x 2 x 7 = 22 x 7</p>

27 <p>Prime factors of 70: 70 = 2 x 5 x 7 = 2 x 5 x 7</p>

26 <p>Prime factors of 70: 70 = 2 x 5 x 7 = 2 x 5 x 7</p>

28 <p><strong>Step 2:</strong>Now, identify the common prime factors.</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors.</p>

29 <p>The common prime factors are: 2 x 7 = 21 x 7</p>

28 <p>The common prime factors are: 2 x 7 = 21 x 7</p>

30 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 7 = 14.</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 7 = 14.</p>

31 <p>The Greatest Common Factor of 28 and 70 is 14.</p>

30 <p>The Greatest Common Factor of 28 and 70 is 14.</p>

32 <h3>GCF of 28 and 70 Using Division Method or Euclidean Algorithm Method</h3>

31 <h3>GCF of 28 and 70 Using Division Method or Euclidean Algorithm Method</h3>

33 <p>Find the GCF of 28 and 70 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

32 <p>Find the GCF of 28 and 70 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

35 <p>Here, divide 70 by 28 70 ÷ 28 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 70 - (28 x 2) = 14</p>

34 <p>Here, divide 70 by 28 70 ÷ 28 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 70 - (28 x 2) = 14</p>

36 <p>The remainder is 14, not zero, so continue the process</p>

35 <p>The remainder is 14, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (28) by the previous remainder (14)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (28) by the previous remainder (14)</p>

38 <p>Divide 28 by 14 28 ÷ 14 = 2 (quotient), remainder = 28 - (14 x 2) = 0</p>

37 <p>Divide 28 by 14 28 ÷ 14 = 2 (quotient), remainder = 28 - (14 x 2) = 0</p>

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

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

40 <p>The GCF of 28 and 70 is 14.</p>

39 <p>The GCF of 28 and 70 is 14.</p>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 28 and 70</h2>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 28 and 70</h2>

42 <p>Finding GCF of 28 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

41 <p>Finding GCF of 28 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

43 <h3>Problem 1</h3>

42 <h3>Problem 1</h3>

44 <p>A gardener has 28 roses and 70 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

43 <p>A gardener has 28 roses and 70 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

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

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

46 <p>We should find the GCF of 28 and 70 GCF of 28 and 70</p>

45 <p>We should find the GCF of 28 and 70 GCF of 28 and 70</p>

47 <p>2 x 7 = 14.</p>

46 <p>2 x 7 = 14.</p>

48 <p>There are 14 equal bouquets</p>

47 <p>There are 14 equal bouquets</p>

49 <p>28 ÷ 14 = 2</p>

48 <p>28 ÷ 14 = 2</p>

50 <p>70 ÷ 14 = 5</p>

49 <p>70 ÷ 14 = 5</p>

51 <p>There will be 14 bouquets, and each bouquet gets 2 roses and 5 tulips.</p>

50 <p>There will be 14 bouquets, and each bouquet gets 2 roses and 5 tulips.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>As the GCF of 28 and 70 is 14, the gardener can make 14 bouquets.</p>

52 <p>As the GCF of 28 and 70 is 14, the gardener can make 14 bouquets.</p>

54 <p>Now divide 28 and 70 by 14.</p>

53 <p>Now divide 28 and 70 by 14.</p>

55 <p>Each bouquet gets 2 roses and 5 tulips.</p>

54 <p>Each bouquet gets 2 roses and 5 tulips.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>A chef has 28 apples and 70 oranges. She wants to make fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?</p>

57 <p>A chef has 28 apples and 70 oranges. She wants to make fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?</p>

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

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

60 <p>GCF of 28 and 70</p>

59 <p>GCF of 28 and 70</p>

61 <p>2 x 7 = 14.</p>

60 <p>2 x 7 = 14.</p>

62 <p>So each basket will have 14 fruits.</p>

61 <p>So each basket will have 14 fruits.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>There are 28 apples and 70 oranges.</p>

63 <p>There are 28 apples and 70 oranges.</p>

65 <p>To find the total number of fruits in each basket, we should find the GCF of 28 and 70.</p>

64 <p>To find the total number of fruits in each basket, we should find the GCF of 28 and 70.</p>

66 <p>There will be 14 fruits in each basket.</p>

65 <p>There will be 14 fruits in each basket.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 3</h3>

67 <h3>Problem 3</h3>

69 <p>A tailor has 28 meters of green ribbon and 70 meters of yellow ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

68 <p>A tailor has 28 meters of green ribbon and 70 meters of yellow ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

71 <p>For calculating the longest equal length, we have to calculate the GCF of 28 and 70</p>

70 <p>For calculating the longest equal length, we have to calculate the GCF of 28 and 70</p>

72 <p>The GCF of 28 and 70</p>

71 <p>The GCF of 28 and 70</p>

73 <p>2 x 7 = 14.</p>

72 <p>2 x 7 = 14.</p>

74 <p>The ribbon is 14 meters long.</p>

73 <p>The ribbon is 14 meters long.</p>

75 <h3>Explanation</h3>

74 <h3>Explanation</h3>

76 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 28 and 70, which is 14. The length of each piece of the ribbon will be 14 meters.</p>

75 <p>For calculating the longest length of the ribbon, first, we need to calculate the GCF of 28 and 70, which is 14. The length of each piece of the ribbon will be 14 meters.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h3>Problem 4</h3>

77 <h3>Problem 4</h3>

79 <p>A carpenter has two wooden planks, one 28 cm long and the other 70 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>

78 <p>A carpenter has two wooden planks, one 28 cm long and the other 70 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>

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

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

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

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

82 <p>GCF of 28 and 70</p>

81 <p>GCF of 28 and 70</p>

83 <p>2 x 7 = 14.</p>

82 <p>2 x 7 = 14.</p>

84 <p>The longest length of each piece is 14 cm.</p>

83 <p>The longest length of each piece is 14 cm.</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

86 <p>To find the longest length of each piece of the two wooden planks, 28 cm and 70 cm, respectively, we have to find the GCF of 28 and 70, which is 14 cm.</p>

85 <p>To find the longest length of each piece of the two wooden planks, 28 cm and 70 cm, respectively, we have to find the GCF of 28 and 70, which is 14 cm.</p>

87 <p>The longest length of each piece is 14 cm.</p>

86 <p>The longest length of each piece is 14 cm.</p>

88 <p>Well explained 👍</p>

87 <p>Well explained 👍</p>

89 <h3>Problem 5</h3>

88 <h3>Problem 5</h3>

90 <p>If the GCF of 28 and 'b' is 14, and the LCM is 140. Find 'b'.</p>

89 <p>If the GCF of 28 and 'b' is 14, and the LCM is 140. Find 'b'.</p>

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

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

92 <p>The value of 'b' is 70.</p>

91 <p>The value of 'b' is 70.</p>

93 <h3>Explanation</h3>

92 <h3>Explanation</h3>

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

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

95 <p>14 x 140 = 28 x b</p>

94 <p>14 x 140 = 28 x b</p>

96 <p>1960 = 28b</p>

95 <p>1960 = 28b</p>

97 <p>b = 1960 ÷ 28 = 70</p>

96 <p>b = 1960 ÷ 28 = 70</p>

98 <p>Well explained 👍</p>

97 <p>Well explained 👍</p>

99 <h2>FAQs on the Greatest Common Factor of 28 and 70</h2>

98 <h2>FAQs on the Greatest Common Factor of 28 and 70</h2>

100 <h3>1.What is the LCM of 28 and 70?</h3>

99 <h3>1.What is the LCM of 28 and 70?</h3>

101 <p>The LCM of 28 and 70 is 140.</p>

100 <p>The LCM of 28 and 70 is 140.</p>

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

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

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

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

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

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

105 <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>

104 <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>

106 <h3>4.What is the prime factorization of 70?</h3>

105 <h3>4.What is the prime factorization of 70?</h3>

107 <p>The prime factorization of 70 is 2 x 5 x 7.</p>

106 <p>The prime factorization of 70 is 2 x 5 x 7.</p>

108 <h3>5.Are 28 and 70 prime numbers?</h3>

107 <h3>5.Are 28 and 70 prime numbers?</h3>

109 <p>No, 28 and 70 are not prime numbers because both of them have more than two factors.</p>

108 <p>No, 28 and 70 are not prime numbers because both of them have more than two factors.</p>

110 <h2>Important Glossaries for GCF of 28 and 70</h2>

109 <h2>Important Glossaries for GCF of 28 and 70</h2>

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

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

112 </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>

111 </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>

113 </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 35 are 5 and 7.</li>

112 </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 35 are 5 and 7.</li>

114 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.</li>

113 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.</li>

115 </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 70 is 140.</li>

114 </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 70 is 140.</li>

116 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 28 and 70 is 14, as it is their largest common factor that divides the numbers completely.</li>

115 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 28 and 70 is 14, as it is their largest common factor that divides the numbers completely.</li>

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

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

118 <p>▶</p>

117 <p>▶</p>

119 <h2>Hiralee Lalitkumar Makwana</h2>

118 <h2>Hiralee Lalitkumar Makwana</h2>

120 <h3>About the Author</h3>

119 <h3>About the Author</h3>

121 <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>

120 <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>

122 <h3>Fun Fact</h3>

121 <h3>Fun Fact</h3>

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

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