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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 the items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 69 and 84.</p>

4 <h2>What is the GCF of 69 and 84?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>69 and 84 is 3. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. 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 69 and 84?</h2>

8 <p>To find the GCF of 69 and 84, 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 69 and 84 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 69 and 84 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 69 = 1, 3, 23, 69.</p>

16 <p>Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 69 and 84: 1, 3.</p>

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

19 <p>The GCF of 69 and 84 is 3.</p>

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22 <h2>GCF of 69 and 84 Using Prime Factorization</h2>

21 <h2>GCF of 69 and 84 Using Prime Factorization</h2>

23 <p>To find the GCF of 69 and 84 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 69 and 84 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 69: 69 = 3 x 23</p>

24 <p>Prime Factors of 69: 69 = 3 x 23</p>

26 <p>Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7</p>

25 <p>Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors The only common prime factor is: 3</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The only common prime factor is: 3</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3. The Greatest Common Factor of 69 and 84 is 3.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 3 = 3. The Greatest Common Factor of 69 and 84 is 3.</p>

29 <h2>GCF of 69 and 84 Using Division Method or Euclidean Algorithm Method</h2>

28 <h2>GCF of 69 and 84 Using Division Method or Euclidean Algorithm Method</h2>

30 <p>Find the GCF of 69 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

29 <p>Find the GCF of 69 and 84 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 69 84 ÷ 69 = 1 (<a>quotient</a>),</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 69 84 ÷ 69 = 1 (<a>quotient</a>),</p>

32 <p>The<a>remainder</a>is calculated as 84 - (69×1) = 15</p>

31 <p>The<a>remainder</a>is calculated as 84 - (69×1) = 15</p>

33 <p>The remainder is 15, not zero, so continue the process</p>

32 <p>The remainder is 15, not zero, so continue the process</p>

34 <p><strong>Step 2:</strong>Now divide the previous divisor (69) by the previous remainder (15)</p>

33 <p><strong>Step 2:</strong>Now divide the previous divisor (69) by the previous remainder (15)</p>

35 <p>Divide 69 by 15 69 ÷ 15 = 4 (quotient), remainder = 69 - (15×4) = 9</p>

34 <p>Divide 69 by 15 69 ÷ 15 = 4 (quotient), remainder = 69 - (15×4) = 9</p>

36 <p><strong>Step 3:</strong>Divide the previous divisor (15) by the previous remainder (9)</p>

35 <p><strong>Step 3:</strong>Divide the previous divisor (15) by the previous remainder (9)</p>

37 <p>Divide 15 by 9 15 ÷ 9 = 1 (quotient), remainder = 15 - (9×1) = 6</p>

36 <p>Divide 15 by 9 15 ÷ 9 = 1 (quotient), remainder = 15 - (9×1) = 6</p>

38 <p><strong>Step 4:</strong>Divide the previous divisor (9) by the previous remainder (6)</p>

37 <p><strong>Step 4:</strong>Divide the previous divisor (9) by the previous remainder (6)</p>

39 <p>Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 - (6×1) = 3</p>

38 <p>Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 - (6×1) = 3</p>

40 <p><strong>Step 5:</strong>Divide the previous divisor (6) by the previous remainder (3)</p>

39 <p><strong>Step 5:</strong>Divide the previous divisor (6) by the previous remainder (3)</p>

41 <p>Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

40 <p>Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0</p>

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

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

43 <p>The GCF of 69 and 84 is 3.</p>

42 <p>The GCF of 69 and 84 is 3.</p>

44 <h2>Common Mistakes and How to Avoid Them in GCF of 69 and 84</h2>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 69 and 84</h2>

45 <p>Finding the GCF of 69 and 84 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

44 <p>Finding the GCF of 69 and 84 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

46 <h3>Problem 1</h3>

45 <h3>Problem 1</h3>

47 <p>A teacher has 69 students and 84 notebooks. She wants to group them into equal sets, with the largest number of items in each group. How many students and notebooks will be in each group?</p>

46 <p>A teacher has 69 students and 84 notebooks. She wants to group them into equal sets, with the largest number of items in each group. How many students and notebooks will be in each group?</p>

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

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

49 <p>We should find the GCF of 69 and 84 GCF of 69 and 84 is 3.</p>

48 <p>We should find the GCF of 69 and 84 GCF of 69 and 84 is 3.</p>

50 <p>There are 3 equal groups 69 ÷ 3 = 23 84 ÷ 3 = 28</p>

49 <p>There are 3 equal groups 69 ÷ 3 = 23 84 ÷ 3 = 28</p>

51 <p>There will be 3 groups, and each group gets 23 students and 28 notebooks.</p>

50 <p>There will be 3 groups, and each group gets 23 students and 28 notebooks.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>As the GCF of 69 and 84 is 3, the teacher can make 3 groups.</p>

52 <p>As the GCF of 69 and 84 is 3, the teacher can make 3 groups.</p>

54 <p>Now divide 69 and 84 by 3.</p>

53 <p>Now divide 69 and 84 by 3.</p>

55 <p>Each group gets 23 students and 28 notebooks.</p>

54 <p>Each group gets 23 students and 28 notebooks.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>A school has 69 red chairs and 84 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>

57 <p>A school has 69 red chairs and 84 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>

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

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

60 <p>GCF of 69 and 84 is 3. So each row will have 3 chairs.</p>

59 <p>GCF of 69 and 84 is 3. So each row will have 3 chairs.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>There are 69 red and 84 blue chairs.</p>

61 <p>There are 69 red and 84 blue chairs.</p>

63 <p>To find the total number of chairs in each row, we should find the GCF of 69 and 84.</p>

62 <p>To find the total number of chairs in each row, we should find the GCF of 69 and 84.</p>

64 <p>There will be 3 chairs in each row.</p>

63 <p>There will be 3 chairs in each row.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

65 <h3>Problem 3</h3>

67 <p>A tailor has 69 meters of red ribbon and 84 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>

66 <p>A tailor has 69 meters of red ribbon and 84 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>

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

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

69 <p>For calculating the longest equal length, we have to calculate the GCF of 69 and 84</p>

68 <p>For calculating the longest equal length, we have to calculate the GCF of 69 and 84</p>

70 <p>The GCF of 69 and 84 is 3.</p>

69 <p>The GCF of 69 and 84 is 3.</p>

71 <p>The ribbon pieces are 3 meters long.</p>

70 <p>The ribbon pieces are 3 meters long.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>For calculating the longest length of the ribbon, first we need to calculate the GCF of 69 and 84, which is 3.</p>

72 <p>For calculating the longest length of the ribbon, first we need to calculate the GCF of 69 and 84, which is 3.</p>

74 <p>The length of each piece of the ribbon will be 3 meters.</p>

73 <p>The length of each piece of the ribbon will be 3 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 planks, one 69 cm long and the other 84 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 planks, one 69 cm long and the other 84 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 GCF of 69 and 84 is 3. The longest length of each piece is 3 cm.</p>

78 <p>The carpenter needs the longest piece of wood GCF of 69 and 84 is 3. The longest length of each piece is 3 cm.</p>

80 <h3>Explanation</h3>

79 <h3>Explanation</h3>

81 <p>To find the longest length of each piece of the two wooden planks, 69 cm and 84 cm, respectively, we have to find the GCF of 69 and 84, which is 3 cm.</p>

80 <p>To find the longest length of each piece of the two wooden planks, 69 cm and 84 cm, respectively, we have to find the GCF of 69 and 84, which is 3 cm.</p>

82 <p>The longest length of each piece is 3 cm.</p>

81 <p>The longest length of each piece is 3 cm.</p>

83 <p>Well explained 👍</p>

82 <p>Well explained 👍</p>

84 <h3>Problem 5</h3>

83 <h3>Problem 5</h3>

85 <p>If the GCF of 69 and ‘a’ is 3, and the LCM is 966, find ‘a’.</p>

84 <p>If the GCF of 69 and ‘a’ is 3, and the LCM is 966, find ‘a’.</p>

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

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

87 <p>The value of ‘a’ is 42.</p>

86 <p>The value of ‘a’ is 42.</p>

88 <h3>Explanation</h3>

87 <h3>Explanation</h3>

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

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

90 <p>3 × 966 = 69 × a</p>

89 <p>3 × 966 = 69 × a</p>

91 <p>2898 = 69a</p>

90 <p>2898 = 69a</p>

92 <p>a = 2898 ÷ 69 = 42</p>

91 <p>a = 2898 ÷ 69 = 42</p>

93 <p>Well explained 👍</p>

92 <p>Well explained 👍</p>

94 <h2>FAQs on the Greatest Common Factor of 69 and 84</h2>

93 <h2>FAQs on the Greatest Common Factor of 69 and 84</h2>

95 <h3>1.What is the LCM of 69 and 84?</h3>

94 <h3>1.What is the LCM of 69 and 84?</h3>

96 <p>The LCM of 69 and 84 is 1932.</p>

95 <p>The LCM of 69 and 84 is 1932.</p>

97 <h3>2.Is 69 divisible by 3?</h3>

96 <h3>2.Is 69 divisible by 3?</h3>

98 <p>Yes, 69 is divisible by 3 because the<a>sum</a>of its digits (6+9=15) is divisible by 3.</p>

97 <p>Yes, 69 is divisible by 3 because the<a>sum</a>of its digits (6+9=15) is divisible by 3.</p>

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

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

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>

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>

101 <h3>4.What is the prime factorization of 84?</h3>

100 <h3>4.What is the prime factorization of 84?</h3>

102 <p>The prime factorization of 84 is 2² x 3 x 7.</p>

101 <p>The prime factorization of 84 is 2² x 3 x 7.</p>

103 <h3>5.Are 69 and 84 prime numbers?</h3>

102 <h3>5.Are 69 and 84 prime numbers?</h3>

104 <p>No, 69 and 84 are not prime numbers because both of them have more than two factors.</p>

103 <p>No, 69 and 84 are not prime numbers because both of them have more than two factors.</p>

105 <h2>Important Glossaries for GCF of 69 and 84</h2>

104 <h2>Important Glossaries for GCF of 69 and 84</h2>

106 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>

105 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</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 4 are 4, 8, 12, 16, 20, and so on.</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 4 are 4, 8, 12, 16, 20, and so on.</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 15 are 3 and 5.</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 15 are 3 and 5.</li>

109 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5, and the quotient is 1.</li>

108 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5, and the quotient is 1.</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 69 and 84 is 1932.</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 69 and 84 is 1932.</li>

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

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

112 <p>▶</p>

111 <p>▶</p>

113 <h2>Hiralee Lalitkumar Makwana</h2>

112 <h2>Hiralee Lalitkumar Makwana</h2>

114 <h3>About the Author</h3>

113 <h3>About the Author</h3>

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>

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>

116 <h3>Fun Fact</h3>

115 <h3>Fun Fact</h3>

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

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