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2 <p>Last updated on<strong>September 19, 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 to schedule events. In this topic, we will learn about the GCF of 45 and 20.</p>

4 <h2>What is the GCF of 45 and 20?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>45 and 20 is 5. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

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

7 <h2>How to find the GCF of 45 and 20?</h2>

8 <p>To find the GCF of 45 and 20, 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><h2>GCF of 45 and 20 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 45 and 20 using the listing of<a>factors</a>:</p>

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

15 <p>Factors of 45 = 1, 3, 5, 9, 15, 45.</p>

16 <p>Factors of 20 = 1, 2, 4, 5, 10, 20.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 45 and 20: 1, 5.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 5.</p>

19 <p>The GCF of 45 and 20 is 5.</p>

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22 <h2>GCF of 45 and 20 Using Prime Factorization</h2>

21 <h2>GCF of 45 and 20 Using Prime Factorization</h2>

23 <p>To find the GCF of 45 and 20 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 45 and 20 using the 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 45: 45 = 3 × 3 × 5 = 3² × 5</p>

24 <p>Prime Factors of 45: 45 = 3 × 3 × 5 = 3² × 5</p>

26 <p>Prime Factors of 20: 20 = 2 × 2 × 5 = 2² × 5</p>

25 <p>Prime Factors of 20: 20 = 2 × 2 × 5 = 2² × 5</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 5</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 5</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

29 <p>The GCF of 45 and 20 is 5.</p>

28 <p>The GCF of 45 and 20 is 5.</p>

30 <h2>GCF of 45 and 20 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 45 and 20 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 45 and 20 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 45 and 20 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 Here, divide 45 by 20 45 ÷ 20 = 2 (<a>quotient</a>),</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 45 by 20 45 ÷ 20 = 2 (<a>quotient</a>),</p>

33 <p>The<a>remainder</a>is calculated as 45 - (20×2) = 5</p>

32 <p>The<a>remainder</a>is calculated as 45 - (20×2) = 5</p>

34 <p>The remainder is 5, not zero, so continue the process</p>

33 <p>The remainder is 5, not zero, so continue the process</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (20) by the previous remainder (5)</p>

34 <p><strong>Step 2:</strong>Now divide the previous divisor (20) by the previous remainder (5)</p>

36 <p>Divide 20 by 5 20 ÷ 5 = 4 (quotient), remainder = 20 - (5×4) = 0</p>

35 <p>Divide 20 by 5 20 ÷ 5 = 4 (quotient), remainder = 20 - (5×4) = 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 45 and 20 is 5.</p>

37 <p>The GCF of 45 and 20 is 5.</p>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 45 and 20</h2>

38 <h2>Common Mistakes and How to Avoid Them in GCF of 45 and 20</h2>

40 <p>Finding the GCF of 45 and 20 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 the GCF of 45 and 20 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 gardener has 45 roses and 20 tulips. She wants to create bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

41 <p>A gardener has 45 roses and 20 tulips. She wants to create bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

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

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

44 <p>We should find the GCF of 45 and 20. GCF of 45 and 20 is 5.</p>

43 <p>We should find the GCF of 45 and 20. GCF of 45 and 20 is 5.</p>

45 <p>There are 5 flowers in each bouquet. 45 ÷ 5 = 9 20 ÷ 5 = 4</p>

44 <p>There are 5 flowers in each bouquet. 45 ÷ 5 = 9 20 ÷ 5 = 4</p>

46 <p>There will be 5 bouquets, and each bouquet gets 9 roses and 4 tulips.</p>

45 <p>There will be 5 bouquets, and each bouquet gets 9 roses and 4 tulips.</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>As the GCF of 45 and 20 is 5, the gardener can make 5 bouquets.</p>

47 <p>As the GCF of 45 and 20 is 5, the gardener can make 5 bouquets.</p>

49 <p>Now divide 45 and 20 by 5.</p>

48 <p>Now divide 45 and 20 by 5.</p>

50 <p>Each bouquet gets 9 roses and 4 tulips.</p>

49 <p>Each bouquet gets 9 roses and 4 tulips.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 2</h3>

51 <h3>Problem 2</h3>

53 <p>A school has 45 desks and 20 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?</p>

52 <p>A school has 45 desks and 20 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?</p>

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

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

55 <p>GCF of 45 and 20 is 5.</p>

54 <p>GCF of 45 and 20 is 5.</p>

56 <p>So each row will have 5 items.</p>

55 <p>So each row will have 5 items.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>There are 45 desks and 20 chairs.</p>

57 <p>There are 45 desks and 20 chairs.</p>

59 <p>To find the total number of items in each row, we should find the GCF of 45 and 20.</p>

58 <p>To find the total number of items in each row, we should find the GCF of 45 and 20.</p>

60 <p>There will be 5 items in each row.</p>

59 <p>There will be 5 items in each row.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

61 <h3>Problem 3</h3>

63 <p>A tailor has 45 meters of fabric and 20 meters of lace. She wants to cut both into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

62 <p>A tailor has 45 meters of fabric and 20 meters of lace. She wants to cut both into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

65 <p>For calculating the longest equal length, we have to calculate the GCF of 45 and 20.</p>

64 <p>For calculating the longest equal length, we have to calculate the GCF of 45 and 20.</p>

66 <p>The GCF of 45 and 20 is 5.</p>

65 <p>The GCF of 45 and 20 is 5.</p>

67 <p>Each piece is 5 meters long.</p>

66 <p>Each piece is 5 meters long.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>For calculating the longest length of the fabric and lace, first we need to calculate the GCF of 45 and 20, which is 5.</p>

68 <p>For calculating the longest length of the fabric and lace, first we need to calculate the GCF of 45 and 20, which is 5.</p>

70 <p>The length of each piece will be 5 meters.</p>

69 <p>The length of each piece will be 5 meters.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A carpenter has two wooden planks, one 45 cm long and the other 20 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>

72 <p>A carpenter has two wooden planks, one 45 cm long and the other 20 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>

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

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

75 <p>The carpenter needs the longest piece of wood. GCF of 45 and 20 is 5.</p>

74 <p>The carpenter needs the longest piece of wood. GCF of 45 and 20 is 5.</p>

76 <p>The longest length of each piece is 5 cm.</p>

75 <p>The longest length of each piece is 5 cm.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>To find the longest length of each piece of the two wooden planks, 45 cm and 20 cm, respectively, we have to find the GCF of 45 and 20, which is 5 cm.</p>

77 <p>To find the longest length of each piece of the two wooden planks, 45 cm and 20 cm, respectively, we have to find the GCF of 45 and 20, which is 5 cm.</p>

79 <p>The longest length of each piece is 5 cm.</p>

78 <p>The longest length of each piece is 5 cm.</p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h3>Problem 5</h3>

80 <h3>Problem 5</h3>

82 <p>If the GCF of 45 and ‘b’ is 5, and the LCM is 180, find ‘b’.</p>

81 <p>If the GCF of 45 and ‘b’ is 5, and the LCM is 180, find ‘b’.</p>

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

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

84 <p>The value of ‘b’ is 20.</p>

83 <p>The value of ‘b’ is 20.</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

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

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

87 <p>5 × 180 = 45 × b</p>

86 <p>5 × 180 = 45 × b</p>

88 <p>900 = 45b</p>

87 <p>900 = 45b</p>

89 <p>b = 900 ÷ 45 = 20</p>

88 <p>b = 900 ÷ 45 = 20</p>

90 <p>Well explained 👍</p>

89 <p>Well explained 👍</p>

91 <h2>FAQs on the Greatest Common Factor of 45 and 20</h2>

90 <h2>FAQs on the Greatest Common Factor of 45 and 20</h2>

92 <h3>1.What is the LCM of 45 and 20?</h3>

91 <h3>1.What is the LCM of 45 and 20?</h3>

93 <p>The LCM of 45 and 20 is 180.</p>

92 <p>The LCM of 45 and 20 is 180.</p>

94 <h3>2.Is 45 divisible by 3?</h3>

93 <h3>2.Is 45 divisible by 3?</h3>

95 <p>Yes, 45 is divisible by 3 because the<a>sum</a>of its digits (4+5) is 9, which is divisible by 3.</p>

94 <p>Yes, 45 is divisible by 3 because the<a>sum</a>of its digits (4+5) is 9, which is divisible by 3.</p>

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

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

97 <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>

96 <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>

98 <h3>4.What is the prime factorization of 20?</h3>

97 <h3>4.What is the prime factorization of 20?</h3>

99 <p>The prime factorization of 20 is 2² × 5.</p>

98 <p>The prime factorization of 20 is 2² × 5.</p>

100 <h3>5.Are 45 and 20 prime numbers?</h3>

99 <h3>5.Are 45 and 20 prime numbers?</h3>

101 <p>No, 45 and 20 are not prime numbers because both of them have more than two factors.</p>

100 <p>No, 45 and 20 are not prime numbers because both of them have more than two factors.</p>

102 <h2>Important Glossaries for GCF of 45 and 20</h2>

101 <h2>Important Glossaries for GCF of 45 and 20</h2>

103 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.</li>

102 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.</li>

104 </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, 25, and so on.</li>

103 </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, 25, and so on.</li>

105 </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 45 are 3 and 5.</li>

104 </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 45 are 3 and 5.</li>

106 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2 and the quotient is 3.</li>

105 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2 and the quotient is 3.</li>

107 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 45 and 20 is 180.</li>

106 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 45 and 20 is 180.</li>

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

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

109 <p>▶</p>

108 <p>▶</p>

110 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h3>About the Author</h3>

110 <h3>About the Author</h3>

112 <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>

111 <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>

113 <h3>Fun Fact</h3>

112 <h3>Fun Fact</h3>

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

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