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2 <p>Last updated on<strong>September 17, 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 16.</p>

4 <h2>What is the GCF of 10 and 16?</h2>

5 <p>The<a>greatest common factor</a>of 10 and 16 is 2. 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 16?</h2>

8 <p>To find the GCF of 10 and 16, 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 16 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 10 and 16 using the listing of<a>factors</a>:</p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 10 = 1, 2, 5, 10. Factors of 16 = 1, 2, 4, 8, 16.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 10 and 16: 1, 2.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 2. The GCF of 10 and 16 is 2.</p>

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19 <h2>GCF of 10 and 16 Using Prime Factorization</h2>

18 <h2>GCF of 10 and 16 Using Prime Factorization</h2>

20 <p>To find the GCF of 10 and 16 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 10 and 16 using the Prime Factorization Method, follow these steps:</p>

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

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

22 <p>Prime Factors of 10: 10 = 2 x 5</p>

21 <p>Prime Factors of 10: 10 = 2 x 5</p>

23 <p>Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24</p>

22 <p>Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24</p>

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

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

25 <p><strong>Step 3:</strong>Multiply the common prime factors 2 = 2. The Greatest Common Factor of 10 and 16 is 2.</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 2 = 2. The Greatest Common Factor of 10 and 16 is 2.</p>

26 <h2>GCF of 10 and 16 Using Division Method or Euclidean Algorithm Method</h2>

25 <h2>GCF of 10 and 16 Using Division Method or Euclidean Algorithm Method</h2>

27 <p>Find the GCF of 10 and 16 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p>Find the GCF of 10 and 16 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

29 <p>Here, divide 16 by 10 16 ÷ 10 = 1 (<a>quotient</a>),</p>

28 <p>Here, divide 16 by 10 16 ÷ 10 = 1 (<a>quotient</a>),</p>

30 <p>The<a>remainder</a>is calculated as 16 - (10×1) = 6</p>

29 <p>The<a>remainder</a>is calculated as 16 - (10×1) = 6</p>

31 <p>The remainder is 6, not zero, so continue the process</p>

30 <p>The remainder is 6, not zero, so continue the process</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (10) by the previous remainder (6)</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (10) by the previous remainder (6)</p>

33 <p>Divide 10 by 6 10 ÷ 6 = 1 (quotient), remainder = 10 - (6×1) = 4 Continue the process</p>

32 <p>Divide 10 by 6 10 ÷ 6 = 1 (quotient), remainder = 10 - (6×1) = 4 Continue the process</p>

34 <p><strong>Step 3:</strong>Now divide the previous divisor (6) by the previous remainder (4)</p>

33 <p><strong>Step 3:</strong>Now divide the previous divisor (6) by the previous remainder (4)</p>

35 <p>Divide 6 by 4 6 ÷ 4 = 1 (quotient), remainder = 6 - (4×1) = 2</p>

34 <p>Divide 6 by 4 6 ÷ 4 = 1 (quotient), remainder = 6 - (4×1) = 2</p>

36 <p>Continue the process</p>

35 <p>Continue the process</p>

37 <p><strong>Step 4:</strong>Now divide the previous divisor (4) by the previous remainder (2)</p>

36 <p><strong>Step 4:</strong>Now divide the previous divisor (4) by the previous remainder (2)</p>

38 <p>Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

37 <p>Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

39 <p>The remainder is zero, the divisor will become the GCF. The GCF of 10 and 16 is 2.</p>

38 <p>The remainder is zero, the divisor will become the GCF. The GCF of 10 and 16 is 2.</p>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 16</h2>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 16</h2>

41 <p>Finding GCF of 10 and 16 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

40 <p>Finding GCF of 10 and 16 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

42 <h3>Problem 1</h3>

41 <h3>Problem 1</h3>

43 <p>A gardener has 10 red roses and 16 white roses. She wants to bundle them into bouquets with an equal number of roses in each. How many roses will be in each bouquet?</p>

42 <p>A gardener has 10 red roses and 16 white roses. She wants to bundle them into bouquets with an equal number of roses in each. How many roses will be in each bouquet?</p>

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

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

45 <p>We should find the GCF of 10 and 16 GCF of 10 and 16 2.</p>

44 <p>We should find the GCF of 10 and 16 GCF of 10 and 16 2.</p>

46 <p>There are 2 equal bouquets 10 ÷ 2 = 5</p>

45 <p>There are 2 equal bouquets 10 ÷ 2 = 5</p>

47 <p>16 ÷ 2 = 8</p>

46 <p>16 ÷ 2 = 8</p>

48 <p>There will be 2 bouquets, and each bouquet gets 5 red roses and 8 white roses.</p>

47 <p>There will be 2 bouquets, and each bouquet gets 5 red roses and 8 white roses.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>As the GCF of 10 and 16 is 2, the gardener can make 2 bouquets.</p>

49 <p>As the GCF of 10 and 16 is 2, the gardener can make 2 bouquets.</p>

51 <p>Now divide 10 and 16 by 2. Each bouquet gets 5 red roses and 8 white roses.</p>

50 <p>Now divide 10 and 16 by 2. Each bouquet gets 5 red roses and 8 white roses.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

52 <h3>Problem 2</h3>

54 <p>A chef has 10 lemons and 16 oranges. He wants to arrange them in baskets with the same number of fruits in each. How many fruits will be in each basket?</p>

53 <p>A chef has 10 lemons and 16 oranges. He wants to arrange them in baskets with the same number of fruits in each. How many fruits will be in each basket?</p>

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

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

56 <p>GCF of 10 and 16 2.</p>

55 <p>GCF of 10 and 16 2.</p>

57 <p>So each basket will have 2 fruits.</p>

56 <p>So each basket will have 2 fruits.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>There are 10 lemons and 16 oranges.</p>

58 <p>There are 10 lemons and 16 oranges.</p>

60 <p>To find the total number of fruits in each basket, we should find the GCF of 10 and 16.</p>

59 <p>To find the total number of fruits in each basket, we should find the GCF of 10 and 16.</p>

61 <p>There will be 2 fruits in each basket.</p>

60 <p>There will be 2 fruits in each basket.</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 10 meters of fabric A and 16 meters of fabric B. 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 10 meters of fabric A and 16 meters of fabric B. 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 10 and 16</p>

65 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 16</p>

67 <p>The GCF of 10 and 16 2.</p>

66 <p>The GCF of 10 and 16 2.</p>

68 <p>The fabric piece is 2 meters long.</p>

67 <p>The fabric piece is 2 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 10 and 16 which is 2. The length of each piece of fabric will be 2 meters.</p>

69 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 10 and 16 which is 2. The length of each piece of fabric will be 2 meters.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A carpenter has two wooden planks, one 10 cm long and the other 16 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>

72 <p>A carpenter has two wooden planks, one 10 cm long and the other 16 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>

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

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

75 <p>The carpenter needs the longest piece of wood GCF of 10 and 16 2.</p>

74 <p>The carpenter needs the longest piece of wood GCF of 10 and 16 2.</p>

76 <p>The longest length of each piece is 2 cm.</p>

75 <p>The longest length of each piece is 2 cm.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 16 cm, respectively.</p>

77 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 16 cm, respectively.</p>

79 <p>We have to find the GCF of 10 and 16, which is 2 cm.</p>

78 <p>We have to find the GCF of 10 and 16, which is 2 cm.</p>

80 <p>The longest length of each piece is 2 cm.</p>

79 <p>The longest length of each piece is 2 cm.</p>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h3>Problem 5</h3>

81 <h3>Problem 5</h3>

83 <p>If the GCF of 10 and ‘a’ is 2, and the LCM is 80. Find ‘a’.</p>

82 <p>If the GCF of 10 and ‘a’ is 2, and the LCM is 80. Find ‘a’.</p>

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

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

85 <p>The value of ‘a’ is 16.</p>

84 <p>The value of ‘a’ is 16.</p>

86 <h3>Explanation</h3>

85 <h3>Explanation</h3>

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

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

88 <p>2 × 80 = 10 × a</p>

87 <p>2 × 80 = 10 × a</p>

89 <p>160 = 10a</p>

88 <p>160 = 10a</p>

90 <p>a = 160 ÷ 10 = 16</p>

89 <p>a = 160 ÷ 10 = 16</p>

91 <p>Well explained 👍</p>

90 <p>Well explained 👍</p>

92 <h2>FAQs on the Greatest Common Factor of 10 and 16</h2>

91 <h2>FAQs on the Greatest Common Factor of 10 and 16</h2>

93 <h3>1.What is the LCM of 10 and 16?</h3>

92 <h3>1.What is the LCM of 10 and 16?</h3>

94 <p>The LCM of 10 and 16 is 80.</p>

93 <p>The LCM of 10 and 16 is 80.</p>

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

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

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

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

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

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

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>

97 <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 <h3>4.What is the prime factorization of 16?</h3>

98 <h3>4.What is the prime factorization of 16?</h3>

100 <p>The prime factorization of 16 is 2^4.</p>

99 <p>The prime factorization of 16 is 2^4.</p>

101 <h3>5.Are 10 and 16 prime numbers?</h3>

100 <h3>5.Are 10 and 16 prime numbers?</h3>

102 <p>No, 10 and 16 are not prime numbers because both of them have more than two factors.</p>

101 <p>No, 10 and 16 are not prime numbers because both of them have more than two factors.</p>

103 <h2>Important Glossaries for GCF of 10 and 16</h2>

102 <h2>Important Glossaries for GCF of 10 and 16</h2>

104 <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>

103 <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>

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 5 are 5, 10, 15, 20, and so on.</li>

104 </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>

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 factor of 10 is 2 and 5.</li>

105 </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 factor of 10 is 2 and 5.</li>

107 </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 6, the remainder is 4 and the quotient is 1.</li>

106 </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 6, the remainder is 4 and the quotient is 1.</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 10 and 16 is 80.</li>

107 </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 16 is 80.</li>

109 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 10 and 16 is 2, as it is their largest common factor that divides the numbers completely.</li>

108 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 10 and 16 is 2, as it is their largest common factor that divides the numbers completely.</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>