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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 14 and 18.</p>

4 <h2>What is the GCF of 14 and 18?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>14 and 18 is 2. 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. The GCF of two numbers cannot be negative because divisors are always positive.</p>

6 <h2>How to find the GCF of 14 and 18?</h2>

7 <p>To find the GCF of 14 and 18, 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><h2>GCF of 14 and 18 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 14 and 18 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 14 = 1, 2, 7, 14.</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 14 and 18: 1, 2.</p>

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

18 <p>The largest factor that both numbers have is 2.</p>

19 <p>The GCF of 14 and 18 is 2.</p>

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22 <h3>GCF of 14 and 18 Using Prime Factorization</h3>

21 <h3>GCF of 14 and 18 Using Prime Factorization</h3>

23 <p>To find the GCF of 14 and 18 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 14 and 18 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 14: 14 = 2 x 7</p>

24 <p>Prime Factors of 14: 14 = 2 x 7</p>

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

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

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

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

28 <p>The common prime factor is: 2</p>

27 <p>The common prime factor is: 2</p>

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

28 <p><strong>Step 3:</strong>Multiply the common prime factors 2 = 2</p>

30 <p>The Greatest Common Factor of 14 and 18 is 2.</p>

29 <p>The Greatest Common Factor of 14 and 18 is 2.</p>

31 <h3>GCF of 14 and 18 Using Division Method or Euclidean Algorithm Method</h3>

30 <h3>GCF of 14 and 18 Using Division Method or Euclidean Algorithm Method</h3>

32 <p>Find the GCF of 14 and 18 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 14 and 18 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

34 <p>Here, divide 18 by 14 18 ÷ 14 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 18 - (14×1) = 4</p>

33 <p>Here, divide 18 by 14 18 ÷ 14 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 18 - (14×1) = 4</p>

35 <p>The remainder is 4, not zero, so continue the process</p>

34 <p>The remainder is 4, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (4)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (14) by the previous remainder (4)</p>

37 <p>Divide 14 by 4 14 ÷ 4 = 3 (quotient), remainder = 14 - (4×3) = 2</p>

36 <p>Divide 14 by 4 14 ÷ 4 = 3 (quotient), remainder = 14 - (4×3) = 2</p>

38 <p><strong>Step 3:</strong>Now divide the previous divisor (4) by the previous remainder (2)</p>

37 <p><strong>Step 3:</strong>Now divide the previous divisor (4) by the previous remainder (2)</p>

39 <p>Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

38 <p>Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

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

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

41 <p>The GCF of 14 and 18 is 2.</p>

40 <p>The GCF of 14 and 18 is 2.</p>

42 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 18</h2>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 14 and 18</h2>

43 <p>Finding GCF of 14 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>

42 <p>Finding GCF of 14 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>

44 <h3>Problem 1</h3>

43 <h3>Problem 1</h3>

45 <p>A gardener has 14 rose plants and 18 tulip plants. She wants to arrange them in equal rows, with the largest number of plants in each row. How many plants will be in each row?</p>

44 <p>A gardener has 14 rose plants and 18 tulip plants. She wants to arrange them in equal rows, with the largest number of plants in each row. How many plants will be in each row?</p>

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

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

47 <p>We should find the GCF of 14 and 18.</p>

46 <p>We should find the GCF of 14 and 18.</p>

48 <p>GCF of 14 and 18 is 2.</p>

47 <p>GCF of 14 and 18 is 2.</p>

49 <p>There are 2 equal groups.</p>

48 <p>There are 2 equal groups.</p>

50 <p>14 ÷ 2 = 7</p>

49 <p>14 ÷ 2 = 7</p>

51 <p>18 ÷ 2 = 9</p>

50 <p>18 ÷ 2 = 9</p>

52 <p>There will be 2 groups, and each row gets 7 rose plants and 9 tulip plants.</p>

51 <p>There will be 2 groups, and each row gets 7 rose plants and 9 tulip plants.</p>

53 <h3>Explanation</h3>

52 <h3>Explanation</h3>

54 <p>As the GCF of 14 and 18 is 2, the gardener can make 2 rows.</p>

53 <p>As the GCF of 14 and 18 is 2, the gardener can make 2 rows.</p>

55 <p>Now divide 14 and 18 by 2.</p>

54 <p>Now divide 14 and 18 by 2.</p>

56 <p>Each row gets 7 rose plants and 9 tulip plants.</p>

55 <p>Each row gets 7 rose plants and 9 tulip plants.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 2</h3>

57 <h3>Problem 2</h3>

59 <p>A chef has 14 apples and 18 oranges. He wants to divide them into 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>

58 <p>A chef has 14 apples and 18 oranges. He wants to divide them into 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>

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

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

61 <p>GCF of 14 and 18 is 2. So each basket will have 2 fruits.</p>

60 <p>GCF of 14 and 18 is 2. So each basket will have 2 fruits.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>There are 14 apples and 18 oranges.</p>

62 <p>There are 14 apples and 18 oranges.</p>

64 <p>To find the total number of fruits in each basket, we should find the GCF of 14 and 18.</p>

63 <p>To find the total number of fruits in each basket, we should find the GCF of 14 and 18.</p>

65 <p>There will be 2 fruits in each basket.</p>

64 <p>There will be 2 fruits in each basket.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h3>Problem 3</h3>

66 <h3>Problem 3</h3>

68 <p>A tailor has 14 meters of silk and 18 meters of cotton. 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>

67 <p>A tailor has 14 meters of silk and 18 meters of cotton. 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>

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

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

70 <p>For calculating longest equal length, we have to calculate the GCF of 14 and 18.</p>

69 <p>For calculating longest equal length, we have to calculate the GCF of 14 and 18.</p>

71 <p>The GCF of 14 and 18 is 2.</p>

70 <p>The GCF of 14 and 18 is 2.</p>

72 <p>The fabric is 2 meters long.</p>

71 <p>The fabric is 2 meters long.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 14 and 18, which is 2. The length of each piece of fabric will be 2 meters.</p>

73 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 14 and 18, which is 2. The length of each piece of fabric will be 2 meters.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

75 <h3>Problem 4</h3>

77 <p>A carpenter has two wooden boards, one 14 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>

76 <p>A carpenter has two wooden boards, one 14 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>

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

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

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

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

80 <p>GCF of 14 and 18 is 2.</p>

79 <p>GCF of 14 and 18 is 2.</p>

81 <p>The longest length of each piece is 2 cm.</p>

80 <p>The longest length of each piece is 2 cm.</p>

82 <h3>Explanation</h3>

81 <h3>Explanation</h3>

83 <p>To find the longest length of each piece of the two wooden boards, 14 cm and 18 cm, respectively, we have to find the GCF of 14 and 18, which is 2 cm. The longest length of each piece is 2 cm.</p>

82 <p>To find the longest length of each piece of the two wooden boards, 14 cm and 18 cm, respectively, we have to find the GCF of 14 and 18, which is 2 cm. The longest length of each piece is 2 cm.</p>

84 <p>Well explained 👍</p>

83 <p>Well explained 👍</p>

85 <h3>Problem 5</h3>

84 <h3>Problem 5</h3>

86 <p>If the GCF of 14 and ‘b’ is 2, and the LCM is 126, find ‘b’.</p>

85 <p>If the GCF of 14 and ‘b’ is 2, and the LCM is 126, find ‘b’.</p>

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

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

88 <p>The value of ‘b’ is 18.</p>

87 <p>The value of ‘b’ is 18.</p>

89 <h3>Explanation</h3>

88 <h3>Explanation</h3>

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

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

91 <p>2 × 126 = 14 × b</p>

90 <p>2 × 126 = 14 × b</p>

92 <p>252 = 14b</p>

91 <p>252 = 14b</p>

93 <p>b = 252 ÷ 14 = 18</p>

92 <p>b = 252 ÷ 14 = 18</p>

94 <p>Well explained 👍</p>

93 <p>Well explained 👍</p>

95 <h2>FAQs on the Greatest Common Factor of 14 and 18</h2>

94 <h2>FAQs on the Greatest Common Factor of 14 and 18</h2>

96 <h3>1.What is the LCM of 14 and 18?</h3>

95 <h3>1.What is the LCM of 14 and 18?</h3>

97 <p>The LCM of 14 and 18 is 126.</p>

96 <p>The LCM of 14 and 18 is 126.</p>

98 <h3>2.Is 14 divisible by 2?</h3>

97 <h3>2.Is 14 divisible by 2?</h3>

99 <p>Yes, 14 is divisible by 2 because it is an even number.</p>

98 <p>Yes, 14 is divisible by 2 because it is an even number.</p>

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

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

101 <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>

100 <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>

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

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

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

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

104 <h3>5.Are 14 and 18 prime numbers?</h3>

103 <h3>5.Are 14 and 18 prime numbers?</h3>

105 <p>No, 14 and 18 are not prime numbers because both of them have more than two factors.</p>

104 <p>No, 14 and 18 are not prime numbers because both of them have more than two factors.</p>

106 <h2>Important Glossaries for GCF of 14 and 18</h2>

105 <h2>Important Glossaries for GCF of 14 and 18</h2>

107 <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>

106 <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>

108 </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>

107 </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>

109 </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>

108 </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>

110 </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 5, the remainder is 4 and the quotient is 2.</li>

109 </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 5, the remainder is 4 and the quotient is 2.</li>

111 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 18 is 126.</li>

110 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 18 is 126.</li>

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

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

113 <p>▶</p>

112 <p>▶</p>

114 <h2>Hiralee Lalitkumar Makwana</h2>

113 <h2>Hiralee Lalitkumar Makwana</h2>

115 <h3>About the Author</h3>

114 <h3>About the Author</h3>

116 <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>

115 <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>

117 <h3>Fun Fact</h3>

116 <h3>Fun Fact</h3>

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

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