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1 - <p>124 Learners</p>

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2 <p>Last updated on<strong>September 12, 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 to schedule events. In this topic, we will learn about the GCF of 35 and 49.</p>

4 <h2>What is the GCF of 35 and 49?</h2>

5 <p>The<a>greatest common factor</a>of 35 and 49 is 7. 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 35 and 49?</h2>

7 <p>To find the GCF of 35 and 49, a few methods are described below -</p>

8 <ol><li>Listing Factors</li>

9 <li>Prime Factorization</li>

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

11 </ol><h2>GCF of 35 and 49 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 35 and 49 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 35 = 1, 5, 7, 35</p>

15 <p>Factors of 49 = 1, 7, 49</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>Common factors of 35 and 49: 1, 7</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 7. The GCF of 35 and 49 is 7.</p>

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20 <h2>GCF of 35 and 49 Using Prime Factorization</h2>

19 <h2>GCF of 35 and 49 Using Prime Factorization</h2>

21 <p>To find the GCF of 35 and 49 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 35 and 49 using the Prime Factorization Method, follow these steps:</p>

22 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

23 <p>Prime factors of 35: 35 = 5 × 7</p>

22 <p>Prime factors of 35: 35 = 5 × 7</p>

24 <p>Prime factors of 49: 49 = 7 × 7 = 7²</p>

23 <p>Prime factors of 49: 49 = 7 × 7 = 7²</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 7</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is 7</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factor 7 = 7</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factor 7 = 7</p>

27 <p>The Greatest Common Factor of 35 and 49 is 7.</p>

26 <p>The Greatest Common Factor of 35 and 49 is 7.</p>

28 <h2>GCF of 35 and 49 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 35 and 49 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 35 and 49 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 35 and 49 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 49 by 35 49 ÷ 35 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 49 - (35 × 1) = 14 The remainder is 14, not zero, so continue the process</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 49 by 35 49 ÷ 35 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 49 - (35 × 1) = 14 The remainder is 14, not zero, so continue the process</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (35) by the previous remainder (14) Divide 35 by 14 35 ÷ 14 = 2 (quotient), remainder = 35 - (14 × 2) = 7 The remainder is 7, not zero, so continue the process</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (35) by the previous remainder (14) Divide 35 by 14 35 ÷ 14 = 2 (quotient), remainder = 35 - (14 × 2) = 7 The remainder is 7, not zero, so continue the process</p>

32 <p><strong>Step 3:</strong>Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 - (7 × 2) = 0</p>

31 <p><strong>Step 3:</strong>Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 - (7 × 2) = 0</p>

33 <p>The remainder is zero, the divisor will become the GCF. The GCF of 35 and 49 is 7.</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 35 and 49 is 7.</p>

34 <h2>Common Mistakes and How to Avoid Them in GCF of 35 and 49</h2>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 35 and 49</h2>

35 <p>Finding the GCF of 35 and 49 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

34 <p>Finding the GCF of 35 and 49 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

36 <h3>Problem 1</h3>

35 <h3>Problem 1</h3>

37 <p>A gardener has 35 rose plants and 49 tulip plants. She wants to plant them in rows with the largest possible number of plants per row and the same number of each type in each row. How many plants will be in each row?</p>

36 <p>A gardener has 35 rose plants and 49 tulip plants. She wants to plant them in rows with the largest possible number of plants per row and the same number of each type in each row. How many plants will be in each row?</p>

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

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

39 <p>We should find the GCF of 35 and 49. GCF of 35 and 49 is 7.</p>

38 <p>We should find the GCF of 35 and 49. GCF of 35 and 49 is 7.</p>

40 <p>There are 7 equal groups. 35 ÷ 7 = 5 49 ÷ 7 = 7</p>

39 <p>There are 7 equal groups. 35 ÷ 7 = 5 49 ÷ 7 = 7</p>

41 <p>There will be 7 rows, and each row will have 5 rose plants and 7 tulip plants.</p>

40 <p>There will be 7 rows, and each row will have 5 rose plants and 7 tulip plants.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>As the GCF of 35 and 49 is 7, the gardener can make 7 rows. Now divide 35 and 49 by 7. Each row will have 5 rose plants and 7 tulip plants.</p>

42 <p>As the GCF of 35 and 49 is 7, the gardener can make 7 rows. Now divide 35 and 49 by 7. Each row will have 5 rose plants and 7 tulip plants.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A school has 35 science kits and 49 math kits. They want to distribute them in sets with the same number of kits in each set, using the largest possible number of kits per set. How many kits will be in each set?</p>

45 <p>A school has 35 science kits and 49 math kits. They want to distribute them in sets with the same number of kits in each set, using the largest possible number of kits per set. How many kits will be in each set?</p>

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

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

48 <p>GCF of 35 and 49 is 7. So each set will have 7 kits.</p>

47 <p>GCF of 35 and 49 is 7. So each set will have 7 kits.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>There are 35 science kits and 49 math kits. To find the total number of kits in each set, we should find the GCF of 35 and 49. There will be 7 kits in each set.</p>

49 <p>There are 35 science kits and 49 math kits. To find the total number of kits in each set, we should find the GCF of 35 and 49. There will be 7 kits in each set.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>A tailor has 35 meters of red fabric and 49 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>

52 <p>A tailor has 35 meters of red fabric and 49 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>

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

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

55 <p>For calculating the longest equal length, we have to calculate the GCF of 35 and 49.</p>

54 <p>For calculating the longest equal length, we have to calculate the GCF of 35 and 49.</p>

56 <p>The GCF of 35 and 49 is 7. The length of each piece will be 7 meters.</p>

55 <p>The GCF of 35 and 49 is 7. The length of each piece will be 7 meters.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>To calculate the longest length of the fabric, first we need to calculate the GCF of 35 and 49, which is 7. The length of each piece of the fabric will be 7 meters.</p>

57 <p>To calculate the longest length of the fabric, first we need to calculate the GCF of 35 and 49, which is 7. The length of each piece of the fabric will be 7 meters.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

59 <h3>Problem 4</h3>

61 <p>A carpenter has two wooden planks, one 35 cm long and the other 49 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>

60 <p>A carpenter has two wooden planks, one 35 cm long and the other 49 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>

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

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

63 <p>The carpenter needs the longest piece of wood. GCF of 35 and 49 is 7.</p>

62 <p>The carpenter needs the longest piece of wood. GCF of 35 and 49 is 7.</p>

64 <p>The longest length of each piece is 7 cm.</p>

63 <p>The longest length of each piece is 7 cm.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the longest length of each piece of the two wooden planks, 35 cm and 49 cm, respectively, we have to find the GCF of 35 and 49, which is 7 cm. The longest length of each piece is 7 cm.</p>

65 <p>To find the longest length of each piece of the two wooden planks, 35 cm and 49 cm, respectively, we have to find the GCF of 35 and 49, which is 7 cm. The longest length of each piece is 7 cm.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

67 <h3>Problem 5</h3>

69 <p>If the GCF of 35 and ‘a’ is 7, and the LCM is 245, find ‘a’.</p>

68 <p>If the GCF of 35 and ‘a’ is 7, and the LCM is 245, find ‘a’.</p>

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

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

71 <p>The value of ‘a’ is 49.</p>

70 <p>The value of ‘a’ is 49.</p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

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

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

74 <p>7 × 245 = 35 × a</p>

73 <p>7 × 245 = 35 × a</p>

75 <p>1715 = 35a</p>

74 <p>1715 = 35a</p>

76 <p>a = 1715 ÷ 35 = 49</p>

75 <p>a = 1715 ÷ 35 = 49</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQs on the Greatest Common Factor of 35 and 49</h2>

77 <h2>FAQs on the Greatest Common Factor of 35 and 49</h2>

79 <h3>1.What is the LCM of 35 and 49?</h3>

78 <h3>1.What is the LCM of 35 and 49?</h3>

80 <p>The LCM of 35 and 49 is 245.</p>

79 <p>The LCM of 35 and 49 is 245.</p>

81 <h3>2.Is 35 divisible by 5?</h3>

80 <h3>2.Is 35 divisible by 5?</h3>

82 <p>Yes, 35 is divisible by 5 because it ends in a 5.</p>

81 <p>Yes, 35 is divisible by 5 because it ends in a 5.</p>

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

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

84 <p>The only common factor of<a>co-prime numbers</a>is 1. Therefore, the GCF of any two co-prime numbers is 1.</p>

83 <p>The only common factor of<a>co-prime numbers</a>is 1. Therefore, the GCF of any two co-prime numbers is 1.</p>

85 <h3>4.What is the prime factorization of 49?</h3>

84 <h3>4.What is the prime factorization of 49?</h3>

86 <p>The prime factorization of 49 is 7².</p>

85 <p>The prime factorization of 49 is 7².</p>

87 <h3>5.Are 35 and 49 prime numbers?</h3>

86 <h3>5.Are 35 and 49 prime numbers?</h3>

88 <p>No, 35 and 49 are not<a>prime numbers</a>because both of them have more than two factors.</p>

87 <p>No, 35 and 49 are not<a>prime numbers</a>because both of them have more than two factors.</p>

89 <h2>Important Glossaries for GCF of 35 and 49</h2>

88 <h2>Important Glossaries for GCF of 35 and 49</h2>

90 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 35 are 1, 5, 7, and 35.</li>

89 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 35 are 1, 5, 7, and 35.</li>

91 </ul><ul><li><strong>Prime Factorization:</strong>This is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 49 is 7 × 7.</li>

90 </ul><ul><li><strong>Prime Factorization:</strong>This is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 49 is 7 × 7.</li>

92 </ul><ul><li><strong>Common Factor:</strong>A factor that is common to two or more numbers. For example, the common factors of 35 and 49 are 1 and 7.</li>

91 </ul><ul><li><strong>Common Factor:</strong>A factor that is common to two or more numbers. For example, the common factors of 35 and 49 are 1 and 7.</li>

93 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 49 is divided by 35, the remainder is 14.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 49 is divided by 35, the remainder is 14.</li>

94 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 35 and 49 is 7, as it is their largest common factor that divides the numbers completely.</li>

93 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 35 and 49 is 7, as it is their largest common factor that divides the numbers completely.</li>

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

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

96 <p>▶</p>

95 <p>▶</p>

97 <h2>Hiralee Lalitkumar Makwana</h2>

96 <h2>Hiralee Lalitkumar Makwana</h2>

98 <h3>About the Author</h3>

97 <h3>About the Author</h3>

99 <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>

98 <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>

100 <h3>Fun Fact</h3>

99 <h3>Fun Fact</h3>

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

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