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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 10 and 7.</p>

4 <h2>What is the GCF of 10 and 7?</h2>

5 <p>The<a>greatest common factor</a>of 10 and 7 is 1. 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 10 and 7?</h2>

8 <p>To find the GCF of 10 and 7, 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 10 and 7 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 10 and 7 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 10 = 1, 2, 5, 10.</p>

16 <p>Factors of 7 = 1, 7.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them</p>

18 <p>Common factor of 10 and 7: 1.</p>

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

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

21 <p>The GCF of 10 and 7 is 1.</p>

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24 <h2>GCF of 10 and 7 Using Prime Factorization</h2>

23 <h2>GCF of 10 and 7 Using Prime Factorization</h2>

25 <p>To find the GCF of 10 and 7 using the Prime Factorization Method, follow these steps:</p>

24 <p>To find the GCF of 10 and 7 using the Prime Factorization Method, follow these steps:</p>

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

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

27 <p>Prime Factors of 10: 10 = 2 × 5</p>

26 <p>Prime Factors of 10: 10 = 2 × 5</p>

28 <p>Prime Factors of 7: 7 = 7 (7 is a<a>prime number</a>)</p>

27 <p>Prime Factors of 7: 7 = 7 (7 is a<a>prime number</a>)</p>

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

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

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

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

31 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

30 <p><strong>Step 3:</strong>Multiply the common prime factors</p>

32 <p>Since there are no common prime factors, the GCF is 1.</p>

31 <p>Since there are no common prime factors, the GCF is 1.</p>

33 <p>The Greatest Common Factor of 10 and 7 is 1.</p>

32 <p>The Greatest Common Factor of 10 and 7 is 1.</p>

34 <h2>GCF of 10 and 7 Using Division Method or Euclidean Algorithm Method</h2>

33 <h2>GCF of 10 and 7 Using Division Method or Euclidean Algorithm Method</h2>

35 <p>Find the GCF of 10 and 7 using the Division Method or Euclidean Algorithm Method, follow these steps:</p>

34 <p>Find the GCF of 10 and 7 using the Division Method or Euclidean Algorithm Method, follow these steps:</p>

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

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

37 <p>Here, divide 10 by 7</p>

36 <p>Here, divide 10 by 7</p>

38 <p>10 ÷ 7 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 10 - (7 × 1) = 3</p>

37 <p>10 ÷ 7 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 10 - (7 × 1) = 3</p>

39 <p>The remainder is 3, not zero, so continue the process</p>

38 <p>The remainder is 3, not zero, so continue the process</p>

40 <p><strong>Step 2:</strong>Now divide the previous divisor (7) by the previous remainder (3)</p>

39 <p><strong>Step 2:</strong>Now divide the previous divisor (7) by the previous remainder (3)</p>

41 <p>Divide 7 by 3</p>

40 <p>Divide 7 by 3</p>

42 <p>7 ÷ 3 = 2 (quotient), remainder = 7 - (3 × 2) = 1</p>

41 <p>7 ÷ 3 = 2 (quotient), remainder = 7 - (3 × 2) = 1</p>

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

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

44 <p>Divide 3 by 1</p>

43 <p>Divide 3 by 1</p>

45 <p>3 ÷ 1 = 3 (quotient), remainder = 3 - (1 × 3) = 0</p>

44 <p>3 ÷ 1 = 3 (quotient), remainder = 3 - (1 × 3) = 0</p>

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

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

47 <p>The GCF of 10 and 7 is 1.</p>

46 <p>The GCF of 10 and 7 is 1.</p>

48 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 7</h2>

47 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 7</h2>

49 <p>Finding GCF of 10 and 7 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

48 <p>Finding GCF of 10 and 7 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

50 <h3>Problem 1</h3>

49 <h3>Problem 1</h3>

51 <p>A teacher has 10 apples and 7 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

50 <p>A teacher has 10 apples and 7 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

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

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

53 <p>We should find GCF of 10 and 7.</p>

52 <p>We should find GCF of 10 and 7.</p>

54 <p>GCF of 10 and 7 is 1.</p>

53 <p>GCF of 10 and 7 is 1.</p>

55 <p>There is only 1 group with 10 apples and 7 oranges.</p>

54 <p>There is only 1 group with 10 apples and 7 oranges.</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>As the GCF of 10 and 7 is 1, the teacher can only make 1 group.</p>

56 <p>As the GCF of 10 and 7 is 1, the teacher can only make 1 group.</p>

58 <p>All the apples and oranges remain in that one group as they cannot be further divided into equal sets.</p>

57 <p>All the apples and oranges remain in that one group as they cannot be further divided into equal sets.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 2</h3>

59 <h3>Problem 2</h3>

61 <p>A school has 10 benches and 7 desks. They want to arrange them in rows with the same number of benches and desks in each row, using the largest possible number of benches and desks per row. How many benches and desks will be in each row?</p>

60 <p>A school has 10 benches and 7 desks. They want to arrange them in rows with the same number of benches and desks in each row, using the largest possible number of benches and desks per row. How many benches and desks will be in each row?</p>

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

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

63 <p>GCF of 10 and 7 is 1.</p>

62 <p>GCF of 10 and 7 is 1.</p>

64 <p>So each row will have 1 bench and 1 desk.</p>

63 <p>So each row will have 1 bench and 1 desk.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>There are 10 benches and 7 desks.</p>

65 <p>There are 10 benches and 7 desks.</p>

67 <p>To find the total number of benches and desks in each row, we should find the GCF of 10 and 7.</p>

66 <p>To find the total number of benches and desks in each row, we should find the GCF of 10 and 7.</p>

68 <p>There will be 1 bench and 1 desk in each row.</p>

67 <p>There will be 1 bench and 1 desk in each row.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h3>Problem 3</h3>

69 <h3>Problem 3</h3>

71 <p>A tailor has 10 meters of blue fabric and 7 meters of red 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>

70 <p>A tailor has 10 meters of blue fabric and 7 meters of red 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>

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

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

73 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 7</p>

72 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 7</p>

74 <p>The GCF of 10 and 7 is 1.</p>

73 <p>The GCF of 10 and 7 is 1.</p>

75 <p>Each piece of fabric is 1 meter long.</p>

74 <p>Each piece of fabric is 1 meter long.</p>

76 <h3>Explanation</h3>

75 <h3>Explanation</h3>

77 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 10 and 7 which is 1.</p>

76 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 10 and 7 which is 1.</p>

78 <p>The length of each piece of the fabric will be 1 meter.</p>

77 <p>The length of each piece of the fabric will be 1 meter.</p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h3>Problem 4</h3>

79 <h3>Problem 4</h3>

81 <p>A carpenter has two wooden planks, one 10 cm long and the other 7 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>

80 <p>A carpenter has two wooden planks, one 10 cm long and the other 7 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>

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

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

83 <p>The carpenter needs the longest piece of wood GCF of 10 and 7 is 1.</p>

82 <p>The carpenter needs the longest piece of wood GCF of 10 and 7 is 1.</p>

84 <p>The longest length of each piece is 1 cm.</p>

83 <p>The longest length of each piece is 1 cm.</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

86 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 7 cm, respectively, we have to find the GCF of 10 and 7, which is 1 cm.</p>

85 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 7 cm, respectively, we have to find the GCF of 10 and 7, which is 1 cm.</p>

87 <p>The longest length of each piece is 1 cm.</p>

86 <p>The longest length of each piece is 1 cm.</p>

88 <p>Well explained 👍</p>

87 <p>Well explained 👍</p>

89 <h3>Problem 5</h3>

88 <h3>Problem 5</h3>

90 <p>If the GCF of 10 and ‘a’ is 1, and the LCM is 70, find ‘a’.</p>

89 <p>If the GCF of 10 and ‘a’ is 1, and the LCM is 70, find ‘a’.</p>

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

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

92 <p>The value of ‘a’ is 7.</p>

91 <p>The value of ‘a’ is 7.</p>

93 <h3>Explanation</h3>

92 <h3>Explanation</h3>

94 <p>GCF × LCM = product of the numbers</p>

93 <p>GCF × LCM = product of the numbers</p>

95 <p>1 × 70 = 10 × a</p>

94 <p>1 × 70 = 10 × a</p>

96 <p>70 = 10a</p>

95 <p>70 = 10a</p>

97 <p>a = 70 ÷ 10 = 7</p>

96 <p>a = 70 ÷ 10 = 7</p>

98 <p>Well explained 👍</p>

97 <p>Well explained 👍</p>

99 <h2>FAQs on the Greatest Common Factor of 10 and 7</h2>

98 <h2>FAQs on the Greatest Common Factor of 10 and 7</h2>

100 <h3>1.What is the LCM of 10 and 7?</h3>

99 <h3>1.What is the LCM of 10 and 7?</h3>

101 <p>The LCM of 10 and 7 is 70.</p>

100 <p>The LCM of 10 and 7 is 70.</p>

102 <h3>2.Is 10 divisible by 2?</h3>

101 <h3>2.Is 10 divisible by 2?</h3>

103 <p>Yes, 10 is divisible by 2 because it is an even number.</p>

102 <p>Yes, 10 is divisible by 2 because it is an even number.</p>

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

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

105 <p>The common factor of prime numbers is 1 and the number itself.</p>

104 <p>The common factor of prime numbers is 1 and the number itself.</p>

106 <p>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>

105 <p>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>

107 <h3>4.What is the prime factorization of 7?</h3>

106 <h3>4.What is the prime factorization of 7?</h3>

108 <p>The prime factorization of 7 is simply 7, as it is a prime number.</p>

107 <p>The prime factorization of 7 is simply 7, as it is a prime number.</p>

109 <h3>5.Are 10 and 7 prime numbers?</h3>

108 <h3>5.Are 10 and 7 prime numbers?</h3>

110 <p>No, 10 and 7 are not prime numbers because 10 has more than two factors, while 7 is a prime number.</p>

109 <p>No, 10 and 7 are not prime numbers because 10 has more than two factors, while 7 is a prime number.</p>

111 <h2>Important Glossaries for GCF of 10 and 7</h2>

110 <h2>Important Glossaries for GCF of 10 and 7</h2>

112 <ul><li><strong>Factors</strong>: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

111 <ul><li><strong>Factors</strong>: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

113 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

112 </ul><ul><li><strong>Multiple</strong>: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.</li>

114 </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 10 are 2 and 5.</li>

113 </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 10 are 2 and 5.</li>

115 </ul><ul><li><strong>Remainder</strong>: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

114 </ul><ul><li><strong>Remainder</strong>: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

116 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 7 is 70.</li>

115 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 7 is 70.</li>

117 </ul><ul><li><strong>GCF</strong>: The l argest factor that commonly divides two or more numbers. For example, the GCF of 10 and 7 will be 1, as it is their largest common factor that divides the numbers completely.</li>

116 </ul><ul><li><strong>GCF</strong>: The l argest factor that commonly divides two or more numbers. For example, the GCF of 10 and 7 will be 1, as it is their largest common factor that divides the numbers completely.</li>

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

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

119 <p>▶</p>

118 <p>▶</p>

120 <h2>Hiralee Lalitkumar Makwana</h2>

119 <h2>Hiralee Lalitkumar Makwana</h2>

121 <h3>About the Author</h3>

120 <h3>About the Author</h3>

122 <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>

121 <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>

123 <h3>Fun Fact</h3>

122 <h3>Fun Fact</h3>

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

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