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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 12 and 35.</p>

4 <h2>What is the GCF of 12 and 35?</h2>

5 <p>The<a>greatest common factor</a>of 12 and 35 is 1. 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 12 and 35?</h2>

7 <p>To find the GCF of 12 and 35, a few methods are described below -</p>

8 <ul><li>Listing Factors</li>

9 <li>Prime Factorization</li>

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

11 </ul><h2>GCF of 12 and 35 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 12 and 35 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 12 = 1, 2, 3, 4, 6, 12.</p>

15 <p>Factors of 35 = 1, 5, 7, 35.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factor of 12 and 35: 1.</p>

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

18 <p>The largest factor that both numbers have is 1.</p>

19 <p>The GCF of 12 and 35 is 1.</p>

20 <h3>Explore Our Programs</h3>

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22 <h2>GCF of 12 and 35 Using Prime Factorization</h2>

21 <h2>GCF of 12 and 35 Using Prime Factorization</h2>

23 <p>To find the GCF of 12 and 35 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 12 and 35 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 12: 12 = 2 x 2 x 3 = 2² x 3</p>

24 <p>Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3</p>

26 <p>Prime Factors of 35: 35 = 5 x 7</p>

25 <p>Prime Factors of 35: 35 = 5 x 7</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>There are no common prime factors.</p>

27 <p>There are no common prime factors.</p>

29 <p><strong>Step 3:</strong>Since there are no common prime factors, the GCF is 1.</p>

28 <p><strong>Step 3:</strong>Since there are no common prime factors, the GCF is 1.</p>

30 <p>The Greatest Common Factor of 12 and 35 is 1.</p>

29 <p>The Greatest Common Factor of 12 and 35 is 1.</p>

31 <h2>GCF of 12 and 35 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 12 and 35 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 12 and 35 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 12 and 35 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 35 by 12 35 ÷ 12 = 2 (<a>quotient</a>),</p>

33 <p>Here, divide 35 by 12 35 ÷ 12 = 2 (<a>quotient</a>),</p>

35 <p>The<a>remainder</a>is calculated as 35 - (12×2) = 11</p>

34 <p>The<a>remainder</a>is calculated as 35 - (12×2) = 11</p>

36 <p>The remainder is 11, not zero, so continue the process</p>

35 <p>The remainder is 11, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (12) by the previous remainder (11)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (12) by the previous remainder (11)</p>

38 <p>Divide 12 by 11 12 ÷ 11 = 1 (quotient), remainder = 12 - (11×1) = 1</p>

37 <p>Divide 12 by 11 12 ÷ 11 = 1 (quotient), remainder = 12 - (11×1) = 1</p>

39 <p>The remainder is 1, not zero, so continue the process</p>

38 <p>The remainder is 1, not zero, so continue the process</p>

40 <p><strong>Step 3:</strong>Now divide the previous divisor (11) by the previous remainder (1)</p>

39 <p><strong>Step 3:</strong>Now divide the previous divisor (11) by the previous remainder (1)</p>

41 <p>Divide 11 by 1 11 ÷ 1 = 11 (quotient), remainder = 11 - (1×11) = 0</p>

40 <p>Divide 11 by 1 11 ÷ 1 = 11 (quotient), remainder = 11 - (1×11) = 0</p>

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

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

43 <p>The GCF of 12 and 35 is 1.</p>

42 <p>The GCF of 12 and 35 is 1.</p>

44 <h2>Common Mistakes and How to Avoid Them in GCF of 12 and 35</h2>

43 <h2>Common Mistakes and How to Avoid Them in GCF of 12 and 35</h2>

45 <p>Finding the GCF of 12 and 35 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 12 and 35 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 gardener has 12 roses and 35 tulips. She wants to group them into sets with the largest number of flowers in each group without mixing roses and tulips. How many flowers will be in each group?</p>

46 <p>A gardener has 12 roses and 35 tulips. She wants to group them into sets with the largest number of flowers in each group without mixing roses and tulips. How many flowers 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 12 and 35 GCF of 12 and 35 is 1.</p>

48 <p>We should find the GCF of 12 and 35 GCF of 12 and 35 is 1.</p>

50 <p>There will be 1 flower in each group.</p>

49 <p>There will be 1 flower in each group.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>As the GCF of 12 and 35 is 1, the gardener can only make groups with 1 flower each, so each group will have either a rose or a tulip but not both.</p>

51 <p>As the GCF of 12 and 35 is 1, the gardener can only make groups with 1 flower each, so each group will have either a rose or a tulip but not both.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 2</h3>

53 <h3>Problem 2</h3>

55 <p>A library has 12 fiction books and 35 nonfiction books. They want to arrange them in stacks with the same number of books in each stack, using the largest possible number of books per stack. How many books will be in each stack?</p>

54 <p>A library has 12 fiction books and 35 nonfiction books. They want to arrange them in stacks with the same number of books in each stack, using the largest possible number of books per stack. How many books will be in each stack?</p>

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

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

57 <p>GCF of 12 and 35 is 1.</p>

56 <p>GCF of 12 and 35 is 1.</p>

58 <p>So each stack will have 1 book.</p>

57 <p>So each stack will have 1 book.</p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>There are 12 fiction and 35 nonfiction books.</p>

59 <p>There are 12 fiction and 35 nonfiction books.</p>

61 <p>To find the total number of books in each stack, we should find the GCF of 12 and 35.</p>

60 <p>To find the total number of books in each stack, we should find the GCF of 12 and 35.</p>

62 <p>There will be 1 book in each stack.</p>

61 <p>There will be 1 book in each stack.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>A chef has 12 apples and 35 bananas. She wants to create fruit 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>

64 <p>A chef has 12 apples and 35 bananas. She wants to create fruit 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>

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

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

67 <p>For calculating the largest equal number of fruits, we have to calculate the GCF of 12 and 35 The GCF of 12 and 35 is 1. Each basket will have 1 fruit.</p>

66 <p>For calculating the largest equal number of fruits, we have to calculate the GCF of 12 and 35 The GCF of 12 and 35 is 1. Each basket will have 1 fruit.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>For calculating the largest number of fruits in each basket, first, we need to calculate the GCF of 12 and 35, which is 1.</p>

68 <p>For calculating the largest number of fruits in each basket, first, we need to calculate the GCF of 12 and 35, which is 1.</p>

70 <p>Each basket will have 1 fruit.</p>

69 <p>Each basket will have 1 fruit.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A painter has two rolls of canvas, one 12 meters long and the other 35 meters long. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the length of each piece?</p>

72 <p>A painter has two rolls of canvas, one 12 meters long and the other 35 meters long. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the length of each piece?</p>

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

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

75 <p>The painter needs the longest piece of canvas GCF of 12 and 35 is 1.</p>

74 <p>The painter needs the longest piece of canvas GCF of 12 and 35 is 1.</p>

76 <p>The longest length of each piece is 1 meter.</p>

75 <p>The longest length of each piece is 1 meter.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>To find the longest length of each piece of the two canvas rolls, 12 meters and 35 meters, respectively, we have to find the GCF of 12 and 35, which is 1 meter. The longest length of each piece is 1 meter.</p>

77 <p>To find the longest length of each piece of the two canvas rolls, 12 meters and 35 meters, respectively, we have to find the GCF of 12 and 35, which is 1 meter. The longest length of each piece is 1 meter.</p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h3>Problem 5</h3>

79 <h3>Problem 5</h3>

81 <p>If the GCF of 12 and ‘b’ is 1, and the LCM is 420, find ‘b’.</p>

80 <p>If the GCF of 12 and ‘b’ is 1, and the LCM is 420, find ‘b’.</p>

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

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

83 <p>The value of ‘b’ is 35.</p>

82 <p>The value of ‘b’ is 35.</p>

84 <h3>Explanation</h3>

83 <h3>Explanation</h3>

85 <p>GCF x LCM = product of the numbers 1 × 420 = 12 × b</p>

84 <p>GCF x LCM = product of the numbers 1 × 420 = 12 × b</p>

86 <p>420 = 12b</p>

85 <p>420 = 12b</p>

87 <p>b = 420 ÷ 12 = 35</p>

86 <p>b = 420 ÷ 12 = 35</p>

88 <p>Well explained 👍</p>

87 <p>Well explained 👍</p>

89 <h2>FAQs on the Greatest Common Factor of 12 and 35</h2>

88 <h2>FAQs on the Greatest Common Factor of 12 and 35</h2>

90 <h3>1.What is the LCM of 12 and 35?</h3>

89 <h3>1.What is the LCM of 12 and 35?</h3>

91 <p>The LCM of 12 and 35 is 420.</p>

90 <p>The LCM of 12 and 35 is 420.</p>

92 <h3>2.Is 12 divisible by 3?</h3>

91 <h3>2.Is 12 divisible by 3?</h3>

93 <p>Yes, 12 is divisible by 3 because 12 ÷ 3 = 4.</p>

92 <p>Yes, 12 is divisible by 3 because 12 ÷ 3 = 4.</p>

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

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

95 <p>The common factor of<a>co-prime numbers</a>is 1. Since 1 is the only common factor of any two co-prime numbers, it is said to be the GCF of any two co-prime numbers.</p>

94 <p>The common factor of<a>co-prime numbers</a>is 1. Since 1 is the only common factor of any two co-prime numbers, it is said to be the GCF of any two co-prime numbers.</p>

96 <h3>4.What is the prime factorization of 12?</h3>

95 <h3>4.What is the prime factorization of 12?</h3>

97 <p>The prime factorization of 12 is 2² x 3.</p>

96 <p>The prime factorization of 12 is 2² x 3.</p>

98 <h3>5.Are 12 and 35 prime numbers?</h3>

97 <h3>5.Are 12 and 35 prime numbers?</h3>

99 <p>No, 12 and 35 are not<a>prime numbers</a>because both of them have more than two factors.</p>

98 <p>No, 12 and 35 are not<a>prime numbers</a>because both of them have more than two factors.</p>

100 <h2>Important Glossaries for GCF of 12 and 35</h2>

99 <h2>Important Glossaries for GCF of 12 and 35</h2>

101 <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>

100 <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>

102 <li><strong>Prime Numbers:</strong>Numbers greater than 1 that have no divisors other than 1 and the number itself. For example, 5 and 7 are prime numbers.</li>

101 <li><strong>Prime Numbers:</strong>Numbers greater than 1 that have no divisors other than 1 and the number itself. For example, 5 and 7 are prime numbers.</li>

103 <li><strong>Co-prime Numbers:</strong>Two or more numbers that have no common factors other than 1. For example, 8 and 15 are co-prime.</li>

102 <li><strong>Co-prime Numbers:</strong>Two or more numbers that have no common factors other than 1. For example, 8 and 15 are co-prime.</li>

104 <li><strong>Prime Factorization:</strong>The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3².</li>

103 <li><strong>Prime Factorization:</strong>The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3².</li>

105 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 12 and 35 is 420.</li>

104 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 12 and 35 is 420.</li>

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

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

107 <p>▶</p>

106 <p>▶</p>

108 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h3>About the Author</h3>

108 <h3>About the Author</h3>

110 <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>

109 <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>

111 <h3>Fun Fact</h3>

110 <h3>Fun Fact</h3>

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

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