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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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 90 and 135.</p>

4 <h2>What is the GCF of 90 and 135?</h2>

5 <p>The<a>greatest common factor</a>of 90 and 135 is 45. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers.</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 90 and 135?</h2>

8 <p>To find the GCF of 90 and 135, 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 90 and 135 by Using Listing of Factors</h3>

13 <p>Steps to find the GCF of 90 and 135 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 90 and 135: 1, 3, 5, 9, 15, 45.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 45. The GCF of 90 and 135 is 45.</p>

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19 <h3>GCF of 90 and 135 Using Prime Factorization</h3>

18 <h3>GCF of 90 and 135 Using Prime Factorization</h3>

20 <p>To find the GCF of 90 and 135 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 90 and 135 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 90: 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5 Prime Factors of 135: 135 = 3 × 3 × 3 × 5 = 3³ × 5</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 90: 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5 Prime Factors of 135: 135 = 3 × 3 × 3 × 5 = 3³ × 5</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 3 × 3 × 5 = 3² × 5</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 3 × 3 × 5 = 3² × 5</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors 3² × 5 = 9 × 5 = 45. The Greatest Common Factor of 90 and 135 is 45.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors 3² × 5 = 9 × 5 = 45. The Greatest Common Factor of 90 and 135 is 45.</p>

24 <h3>GCF of 90 and 135 Using Division Method or Euclidean Algorithm Method</h3>

23 <h3>GCF of 90 and 135 Using Division Method or Euclidean Algorithm Method</h3>

25 <p>Find the GCF of 90 and 135 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 90 and 135 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 135 by 90 135 ÷ 90 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 135 - (90×1) = 45 The remainder is 45, not zero, so continue the process</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 135 by 90 135 ÷ 90 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 135 - (90×1) = 45 The remainder is 45, not zero, so continue the process</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (90) by the previous remainder (45) Divide 90 by 45 90 ÷ 45 = 2 (quotient), remainder = 90 - (45×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

26 <p><strong>Step 2:</strong>Now divide the previous divisor (90) by the previous remainder (45) Divide 90 by 45 90 ÷ 45 = 2 (quotient), remainder = 90 - (45×2) = 0 The remainder is zero, the divisor will become the GCF.</p>

28 <p>The GCF of 90 and 135 is 45.</p>

27 <p>The GCF of 90 and 135 is 45.</p>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 90 and 135</h2>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 90 and 135</h2>

30 <p>Finding the GCF of 90 and 135 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

29 <p>Finding the GCF of 90 and 135 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>A chef has 90 apples and 135 oranges. He wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

31 <p>A chef has 90 apples and 135 oranges. He wants to group them into equal sets, with the largest number of items in each group. How many items 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 90 and 135 GCF of 90 and 135 3² × 5 = 9 × 5 = 45. There are 45 equal groups 90 ÷ 45 = 2 135 ÷ 45 = 3 There will be 45 groups, and each group gets 2 apples and 3 oranges.</p>

33 <p>We should find the GCF of 90 and 135 GCF of 90 and 135 3² × 5 = 9 × 5 = 45. There are 45 equal groups 90 ÷ 45 = 2 135 ÷ 45 = 3 There will be 45 groups, and each group gets 2 apples and 3 oranges.</p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

36 <p>As the GCF of 90 and 135 is 45, the chef can make 45 groups.</p>

35 <p>As the GCF of 90 and 135 is 45, the chef can make 45 groups.</p>

37 <p>Now divide 90 and 135 by 45.</p>

36 <p>Now divide 90 and 135 by 45.</p>

38 <p>Each group gets 2 apples and 3 oranges.</p>

37 <p>Each group gets 2 apples and 3 oranges.</p>

39 <p>Well explained 👍</p>

38 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

39 <h3>Problem 2</h3>

41 <p>A school has 90 red chairs and 135 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

40 <p>A school has 90 red chairs and 135 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

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

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

43 <p>GCF of 90 and 135 3² × 5 = 9 × 5 = 45. So each row will have 45 chairs.</p>

42 <p>GCF of 90 and 135 3² × 5 = 9 × 5 = 45. So each row will have 45 chairs.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>There are 90 red and 135 blue chairs.</p>

44 <p>There are 90 red and 135 blue chairs.</p>

46 <p>To find the total number of chairs in each row, we should find the GCF of 90 and 135.</p>

45 <p>To find the total number of chairs in each row, we should find the GCF of 90 and 135.</p>

47 <p>There will be 45 chairs in each row.</p>

46 <p>There will be 45 chairs in each row.</p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

48 <h3>Problem 3</h3>

50 <p>A gardener has 90 meters of red rope and 135 meters of blue rope. She wants to cut both ropes into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

49 <p>A gardener has 90 meters of red rope and 135 meters of blue rope. She wants to cut both ropes into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

52 <p>For calculating the longest equal length, we have to calculate the GCF of 90 and 135 The GCF of 90 and 135 3² × 5 = 9 × 5 = 45. The rope is 45 meters long.</p>

51 <p>For calculating the longest equal length, we have to calculate the GCF of 90 and 135 The GCF of 90 and 135 3² × 5 = 9 × 5 = 45. The rope is 45 meters long.</p>

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 <p>For calculating the longest length of the rope, first we need to calculate the GCF of 90 and 135, which is 45.</p>

53 <p>For calculating the longest length of the rope, first we need to calculate the GCF of 90 and 135, which is 45.</p>

55 <p>The length of each piece of the rope will be 45 meters.</p>

54 <p>The length of each piece of the rope will be 45 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 planks, one 90 cm long and the other 135 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 planks, one 90 cm long and the other 135 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 90 and 135 3² × 5 = 9 × 5 = 45. The longest length of each piece is 45 cm.</p>

59 <p>The carpenter needs the longest piece of wood GCF of 90 and 135 3² × 5 = 9 × 5 = 45. The longest length of each piece is 45 cm.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>To find the longest length of each piece of the two wooden planks, 90 cm and 135 cm, respectively.</p>

61 <p>To find the longest length of each piece of the two wooden planks, 90 cm and 135 cm, respectively.</p>

63 <p>We have to find the GCF of 90 and 135, which is 45 cm.</p>

62 <p>We have to find the GCF of 90 and 135, which is 45 cm.</p>

64 <p>The longest length of each piece is 45 cm.</p>

63 <p>The longest length of each piece is 45 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 90 and ‘a’ is 45, and the LCM is 270. Find ‘a’.</p>

66 <p>If the GCF of 90 and ‘a’ is 45, and the LCM is 270. Find ‘a’.</p>

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

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

69 <p>The value of ‘a’ is 135.</p>

68 <p>The value of ‘a’ is 135.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>GCF × LCM = product of the numbers</p>

70 <p>GCF × LCM = product of the numbers</p>

72 <p>45 × 270 = 90 × a</p>

71 <p>45 × 270 = 90 × a</p>

73 <p>12150 = 90a</p>

72 <p>12150 = 90a</p>

74 <p>a = 12150 ÷ 90</p>

73 <p>a = 12150 ÷ 90</p>

75 <p>= 135</p>

74 <p>= 135</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h2>FAQs on the Greatest Common Factor of 90 and 135</h2>

76 <h2>FAQs on the Greatest Common Factor of 90 and 135</h2>

78 <h3>1.What is the LCM of 90 and 135?</h3>

77 <h3>1.What is the LCM of 90 and 135?</h3>

79 <p>The LCM of 90 and 135 is 270.</p>

78 <p>The LCM of 90 and 135 is 270.</p>

80 <h3>2.Is 90 divisible by 2?</h3>

79 <h3>2.Is 90 divisible by 2?</h3>

81 <p>Yes, 90 is divisible by 2 because it is an even number.</p>

80 <p>Yes, 90 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 135?</h3>

83 <h3>4.What is the prime factorization of 135?</h3>

85 <p>The prime factorization of 135 is 3³ × 5.</p>

84 <p>The prime factorization of 135 is 3³ × 5.</p>

86 <h3>5.Are 90 and 135 prime numbers?</h3>

85 <h3>5.Are 90 and 135 prime numbers?</h3>

87 <p>No, 90 and 135 are not prime numbers because both of them have more than two factors.</p>

86 <p>No, 90 and 135 are not prime numbers because both of them have more than two factors.</p>

88 <h2>Important Glossaries for GCF of 90 and 135</h2>

87 <h2>Important Glossaries for GCF of 90 and 135</h2>

89 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</li>

88 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</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 6 are 6, 12, 18, 24, 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 6 are 6, 12, 18, 24, 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 18 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 18 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 14 is divided by 4, the remainder is 2 and the quotient is 3.</li>

91 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.</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 8 and 12 is 24.</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 8 and 12 is 24.</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>