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2 <p>Last updated on<strong>September 20, 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 36 and 162.</p>

4 <h2>What is the GCF of 36 and 162?</h2>

5 <p>The<a>greatest common factor</a>of 36 and 162 is 18. 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 36 and 162?</h2>

8 <p>To find the GCF of 36 and 162, 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 36 and 162 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 36 and 162 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 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36</p>

16 <p>Factors of 162 = 1, 2, 3, 6, 9, 18, 27, 54, 81, 162</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>Common factors of 36 and 162: 1, 2, 3, 6, 9, 18</p>

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

19 <p>The GCF of 36 and 162 is 18.</p>

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22 <h2>GCF of 36 and 162 Using Prime Factorization</h2>

21 <h2>GCF of 36 and 162 Using Prime Factorization</h2>

23 <p>To find the GCF of 36 and 162 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 36 and 162 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 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>

24 <p>Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>

26 <p>Prime Factors of 162: 162 = 2 x 3 x 3 x 3 x 3 = 2 x 3⁴</p>

25 <p>Prime Factors of 162: 162 = 2 x 3 x 3 x 3 x 3 = 2 x 3⁴</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 factors are: 2 x 3 x 3 = 2 x 3²</p>

27 <p>The common prime factors are: 2 x 3 x 3 = 2 x 3²</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 3² = 2 x 9 = 18.</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 2 x 3² = 2 x 9 = 18.</p>

30 <p>The Greatest Common Factor of 36 and 162 is 18.</p>

29 <p>The Greatest Common Factor of 36 and 162 is 18.</p>

31 <h2>GCF of 36 and 162 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 36 and 162 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 36 and 162 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 36 and 162 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 Here, divide 162 by 36 162 ÷ 36 = 4 (<a>quotient</a>),</p>

32 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 162 by 36 162 ÷ 36 = 4 (<a>quotient</a>),</p>

34 <p>The<a>remainder</a>is calculated as 162 - (36×4) = 18</p>

33 <p>The<a>remainder</a>is calculated as 162 - (36×4) = 18</p>

35 <p>The remainder is 18, not zero, so continue the process</p>

34 <p>The remainder is 18, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (18)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (36) by the previous remainder (18)</p>

37 <p>Divide 36 by 18 36 ÷ 18 = 2 (quotient), remainder = 36 - (18×2) = 0</p>

36 <p>Divide 36 by 18 36 ÷ 18 = 2 (quotient), remainder = 36 - (18×2) = 0</p>

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

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

39 <p>The GCF of 36 and 162 is 18.</p>

38 <p>The GCF of 36 and 162 is 18.</p>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 162</h2>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 36 and 162</h2>

41 <p>Finding the GCF of 36 and 162 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

40 <p>Finding the GCF of 36 and 162 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

42 <h3>Problem 1</h3>

41 <h3>Problem 1</h3>

43 <p>A chef has 36 apples and 162 oranges. He wants to distribute them into equal baskets, with the largest number of items in each basket. How many items will be in each basket?</p>

42 <p>A chef has 36 apples and 162 oranges. He wants to distribute them into equal baskets, with the largest number of items in each basket. How many items will be in each basket?</p>

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

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

45 <p>We should find the GCF of 36 and 162. GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

44 <p>We should find the GCF of 36 and 162. GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

46 <p>There will be 18 items in each basket. 36 ÷ 18 = 2 162 ÷ 18 = 9</p>

45 <p>There will be 18 items in each basket. 36 ÷ 18 = 2 162 ÷ 18 = 9</p>

47 <p>There will be 18 baskets, and each basket gets 2 apples and 9 oranges.</p>

46 <p>There will be 18 baskets, and each basket gets 2 apples and 9 oranges.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>As the GCF of 36 and 162 is 18, the chef can make 18 baskets.</p>

48 <p>As the GCF of 36 and 162 is 18, the chef can make 18 baskets.</p>

50 <p>Now divide 36 and 162 by 18.</p>

49 <p>Now divide 36 and 162 by 18.</p>

51 <p>Each basket gets 2 apples and 9 oranges.</p>

50 <p>Each basket gets 2 apples and 9 oranges.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

52 <h3>Problem 2</h3>

54 <p>A school has 36 red markers and 162 blue markers. They want to arrange them in rows with the same number of markers in each row, using the largest possible number of markers per row. How many markers will be in each row?</p>

53 <p>A school has 36 red markers and 162 blue markers. They want to arrange them in rows with the same number of markers in each row, using the largest possible number of markers per row. How many markers will be in each row?</p>

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

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

56 <p>GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

55 <p>GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

57 <p>So each row will have 18 markers.</p>

56 <p>So each row will have 18 markers.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>There are 36 red and 162 blue markers.</p>

58 <p>There are 36 red and 162 blue markers.</p>

60 <p>To find the total number of markers in each row, we should find the GCF of 36 and 162.</p>

59 <p>To find the total number of markers in each row, we should find the GCF of 36 and 162.</p>

61 <p>There will be 18 markers in each row.</p>

60 <p>There will be 18 markers in each row.</p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

62 <h3>Problem 3</h3>

64 <p>A tailor has 36 meters of red fabric and 162 meters of blue fabric. 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>

63 <p>A tailor has 36 meters of red fabric and 162 meters of blue fabric. 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>

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

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

66 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 162.</p>

65 <p>For calculating the longest equal length, we have to calculate the GCF of 36 and 162.</p>

67 <p>The GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

66 <p>The GCF of 36 and 162 2 x 3² = 2 x 9 = 18.</p>

68 <p>The fabric is 18 meters long.</p>

67 <p>The fabric is 18 meters long.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 36 and 162, which is 18.</p>

69 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 36 and 162, which is 18.</p>

71 <p>The length of each piece of the fabric will be 18 meters.</p>

70 <p>The length of each piece of the fabric will be 18 meters.</p>

72 <p>Well explained 👍</p>

71 <p>Well explained 👍</p>

73 <h3>Problem 4</h3>

72 <h3>Problem 4</h3>

74 <p>A carpenter has two wooden planks, one 36 cm long and the other 162 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>

73 <p>A carpenter has two wooden planks, one 36 cm long and the other 162 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>

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

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

76 <p>The carpenter needs the longest piece of wood. GCF of 36 and 162</p>

75 <p>The carpenter needs the longest piece of wood. GCF of 36 and 162</p>

77 <p>2 x 3² = 2 x 9 = 18.</p>

76 <p>2 x 3² = 2 x 9 = 18.</p>

78 <p>The longest length of each piece is 18 cm.</p>

77 <p>The longest length of each piece is 18 cm.</p>

79 <h3>Explanation</h3>

78 <h3>Explanation</h3>

80 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 162 cm, respectively, we have to find the GCF of 36 and 162, which is 18 cm.</p>

79 <p>To find the longest length of each piece of the two wooden planks, 36 cm and 162 cm, respectively, we have to find the GCF of 36 and 162, which is 18 cm.</p>

81 <p>The longest length of each piece is 18 cm.</p>

80 <p>The longest length of each piece is 18 cm.</p>

82 <p>Well explained 👍</p>

81 <p>Well explained 👍</p>

83 <h3>Problem 5</h3>

82 <h3>Problem 5</h3>

84 <p>If the GCF of 36 and ‘b’ is 18, and the LCM is 324. Find ‘b’.</p>

83 <p>If the GCF of 36 and ‘b’ is 18, and the LCM is 324. Find ‘b’.</p>

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

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

86 <p>The value of ‘b’ is 162.</p>

85 <p>The value of ‘b’ is 162.</p>

87 <h3>Explanation</h3>

86 <h3>Explanation</h3>

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

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

89 <p>18 × 324 = 36 × b</p>

88 <p>18 × 324 = 36 × b</p>

90 <p>5832 = 36b</p>

89 <p>5832 = 36b</p>

91 <p>b = 5832 ÷ 36 = 162</p>

90 <p>b = 5832 ÷ 36 = 162</p>

92 <p>Well explained 👍</p>

91 <p>Well explained 👍</p>

93 <h2>FAQs on the Greatest Common Factor of 36 and 162</h2>

92 <h2>FAQs on the Greatest Common Factor of 36 and 162</h2>

94 <h3>1.What is the LCM of 36 and 162?</h3>

93 <h3>1.What is the LCM of 36 and 162?</h3>

95 <p>The LCM of 36 and 162 is 324.</p>

94 <p>The LCM of 36 and 162 is 324.</p>

96 <h3>2.Is 36 divisible by 2?</h3>

95 <h3>2.Is 36 divisible by 2?</h3>

97 <p>Yes, 36 is divisible by 2 because it is an even number.</p>

96 <p>Yes, 36 is divisible by 2 because it is an even number.</p>

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

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

99 <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 <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 <h3>4.What is the prime factorization of 162?</h3>

99 <h3>4.What is the prime factorization of 162?</h3>

101 <p>The prime factorization of 162 is 2 x 3⁴.</p>

100 <p>The prime factorization of 162 is 2 x 3⁴.</p>

102 <h3>5.Are 36 and 162 prime numbers?</h3>

101 <h3>5.Are 36 and 162 prime numbers?</h3>

103 <p>No, 36 and 162 are not prime numbers because both of them have more than two factors.</p>

102 <p>No, 36 and 162 are not prime numbers because both of them have more than two factors.</p>

104 <h2>Important Glossaries for GCF of 36 and 162</h2>

103 <h2>Important Glossaries for GCF of 36 and 162</h2>

105 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.</li>

104 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.</li>

106 </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>

105 </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>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>

106 </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>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.</li>

107 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.</li>

109 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 162 is 324.</li>

108 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 162 is 324.</li>

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

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

111 <p>▶</p>

110 <p>▶</p>

112 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h2>Hiralee Lalitkumar Makwana</h2>

113 <h3>About the Author</h3>

112 <h3>About the Author</h3>

114 <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 <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 <h3>Fun Fact</h3>

114 <h3>Fun Fact</h3>

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

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