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1 - <p>143 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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 9 and 18.</p>

4 <h2>What is the GCF of 9 and 18?</h2>

5 <p>The<a>greatest common factor</a>of 9 and 18 is 9. 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 9 and 18?</h2>

8 <p>To find the GCF of 9 and 18, a few methods are described below -</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

11 <li>Long Division Method / by Euclidean Algorithm</li>

12 </ol><h2>GCF of 9 and 18 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 9 and 18 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 9 = 1, 3, 9.</p>

15 <p>Factors of 18 = 1, 2, 3, 6, 9, 18.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 9 and 18: 1, 3, 9.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 9. The GCF of 9 and 18 is 9.</p>

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20 <h2>GCF of 9 and 18 Using Prime Factorization</h2>

19 <h2>GCF of 9 and 18 Using Prime Factorization</h2>

21 <p>To find the GCF of 9 and 18 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 9 and 18 using the Prime Factorization Method, follow these steps:</p>

22 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 9: 9 = 3 x 3 = 3²</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 9: 9 = 3 x 3 = 3²</p>

23 <p>Prime Factors of 18: 18 = 2 x 3 x 3 = 2 x 3²</p>

22 <p>Prime Factors of 18: 18 = 2 x 3 x 3 = 2 x 3²</p>

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

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

25 <p><strong>Step 3:</strong>Multiply the common prime factors 3² = 9. The Greatest Common Factor of 9 and 18 is 9.</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 3² = 9. The Greatest Common Factor of 9 and 18 is 9.</p>

26 <h2>GCF of 9 and 18 Using Division Method or Euclidean Algorithm Method</h2>

25 <h2>GCF of 9 and 18 Using Division Method or Euclidean Algorithm Method</h2>

27 <p>Find the GCF of 9 and 18 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p>Find the GCF of 9 and 18 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 18 by 9 18 ÷ 9 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 18 - (9×2) = 0</p>

27 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 18 by 9 18 ÷ 9 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 18 - (9×2) = 0</p>

29 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 9 and 18 is 9.</p>

28 <p>The remainder is zero, so the divisor will become the GCF. The GCF of 9 and 18 is 9.</p>

30 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 18</h2>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 9 and 18</h2>

31 <p>Finding the GCF of 9 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

30 <p>Finding the GCF of 9 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>A teacher has 9 apples and 18 oranges. She 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>

32 <p>A teacher has 9 apples and 18 oranges. She 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>

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

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

35 <p>We should find the GCF of 9 and 18. GCF of 9 and 18 is 9. There are 9 equal groups 9 ÷ 9 = 1 18 ÷ 9 = 2 There will be 9 groups, and each group gets 1 apple and 2 oranges.</p>

34 <p>We should find the GCF of 9 and 18. GCF of 9 and 18 is 9. There are 9 equal groups 9 ÷ 9 = 1 18 ÷ 9 = 2 There will be 9 groups, and each group gets 1 apple and 2 oranges.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

37 <p>As the GCF of 9 and 18 is 9, the teacher can make 9 groups. Now divide 9 and 18 by 9. Each group gets 1 apple and 2 oranges.</p>

36 <p>As the GCF of 9 and 18 is 9, the teacher can make 9 groups. Now divide 9 and 18 by 9. Each group gets 1 apple and 2 oranges.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>A school has 9 red chairs and 18 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>

39 <p>A school has 9 red chairs and 18 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>

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

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

42 <p>GCF of 9 and 18 is 9. So each row will have 9 chairs.</p>

41 <p>GCF of 9 and 18 is 9. So each row will have 9 chairs.</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>There are 9 red and 18 blue chairs. To find the total number of chairs in each row, we should find the GCF of 9 and 18. There will be 9 chairs in each row.</p>

43 <p>There are 9 red and 18 blue chairs. To find the total number of chairs in each row, we should find the GCF of 9 and 18. There will be 9 chairs in each row.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 3</h3>

45 <h3>Problem 3</h3>

47 <p>A tailor has 9 meters of red ribbon and 18 meters of blue 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>

46 <p>A tailor has 9 meters of red ribbon and 18 meters of blue 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>

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

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

49 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 18. The GCF of 9 and 18 is 9. The ribbon is 9 meters long.</p>

48 <p>For calculating the longest equal length, we have to calculate the GCF of 9 and 18. The GCF of 9 and 18 is 9. The ribbon is 9 meters long.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>To calculate the longest length of the ribbon, first, we need to calculate the GCF of 9 and 18, which is 9. The length of each piece of the ribbon will be 9 meters.</p>

50 <p>To calculate the longest length of the ribbon, first, we need to calculate the GCF of 9 and 18, which is 9. The length of each piece of the ribbon will be 9 meters.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 4</h3>

52 <h3>Problem 4</h3>

54 <p>A carpenter has two wooden planks, one 9 cm long and the other 18 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>

53 <p>A carpenter has two wooden planks, one 9 cm long and the other 18 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>

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

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

56 <p>The carpenter needs the longest piece of wood. GCF of 9 and 18 is 9. The longest length of each piece is 9 cm.</p>

55 <p>The carpenter needs the longest piece of wood. GCF of 9 and 18 is 9. The longest length of each piece is 9 cm.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 18 cm, respectively, we have to find the GCF of 9 and 18, which is 9 cm. The longest length of each piece is 9 cm.</p>

57 <p>To find the longest length of each piece of the two wooden planks, 9 cm and 18 cm, respectively, we have to find the GCF of 9 and 18, which is 9 cm. The longest length of each piece is 9 cm.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 5</h3>

59 <h3>Problem 5</h3>

61 <p>If the GCF of 9 and ‘a’ is 3, and the LCM is 27. Find ‘a’.</p>

60 <p>If the GCF of 9 and ‘a’ is 3, and the LCM is 27. Find ‘a’.</p>

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

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

63 <p>The value of ‘a’ is 9.</p>

62 <p>The value of ‘a’ is 9.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>GCF x LCM = product of the numbers 3 × 27 = 9 × a</p>

64 <p>GCF x LCM = product of the numbers 3 × 27 = 9 × a</p>

66 <p>81 = 9a</p>

65 <p>81 = 9a</p>

67 <p>a = 81 ÷ 9 = 9</p>

66 <p>a = 81 ÷ 9 = 9</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h2>FAQs on the Greatest Common Factor of 9 and 18</h2>

68 <h2>FAQs on the Greatest Common Factor of 9 and 18</h2>

70 <h3>1.What is the LCM of 9 and 18?</h3>

69 <h3>1.What is the LCM of 9 and 18?</h3>

71 <p>The LCM of 9 and 18 is 18.</p>

70 <p>The LCM of 9 and 18 is 18.</p>

72 <h3>2.Is 9 divisible by 3?</h3>

71 <h3>2.Is 9 divisible by 3?</h3>

73 <p>Yes, 9 is divisible by 3 because 9 divided by 3 equals 3 with no remainder.</p>

72 <p>Yes, 9 is divisible by 3 because 9 divided by 3 equals 3 with no remainder.</p>

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

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

75 <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>

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>

76 <h3>4.What is the prime factorization of 18?</h3>

75 <h3>4.What is the prime factorization of 18?</h3>

77 <p>The prime factorization of 18 is 2 x 3².</p>

76 <p>The prime factorization of 18 is 2 x 3².</p>

78 <h3>5.Are 9 and 18 prime numbers?</h3>

77 <h3>5.Are 9 and 18 prime numbers?</h3>

79 <p>No, 9 and 18 are not prime numbers because both of them have more than two factors.</p>

78 <p>No, 9 and 18 are not prime numbers because both of them have more than two factors.</p>

80 <h2>Important Glossaries for GCF of 9 and 18</h2>

79 <h2>Important Glossaries for GCF of 9 and 18</h2>

81 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

80 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.</li>

82 </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, 15, and so on.</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, 15, and so on.</li>

83 </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>

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>

84 </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>

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>

85 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 9 and 18 is 18.</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 9 and 18 is 18.</li>

86 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 18 is 9, as it is their largest common factor that divides the numbers completely.</li>

85 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 18 is 9, as it is their largest common factor that divides the numbers completely.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Hiralee Lalitkumar Makwana</h2>

88 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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