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1 - <p>129 Learners</p>

1 + <p>153 Learners</p>

2 <p>Last updated on<strong>September 11, 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 schedule events. In this topic, we will learn about the GCF of 16 and 100.</p>

4 <h2>What is the GCF of 16 and 100?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>16 and 100 is 4. 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. The GCF of two numbers cannot be negative because divisors are always positive.</p>

6 <h2>How to find the GCF of 16 and 100?</h2>

7 <p>To find the GCF of 16 and 100, 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 16 and 100 by Using Listing of Factors</h2>

12 <p>Steps to find the GCF of 16 and 100 using the listing of<a>factors</a></p>

13 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.</p>

14 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 16 and 100: 1, 2, 4.</p>

15 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 4. The GCF of 16 and 100 is 4.</p>

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18 <h2>GCF of 16 and 100 Using Prime Factorization</h2>

17 <h2>GCF of 16 and 100 Using Prime Factorization</h2>

19 <p>To find the GCF of 16 and 100 using the Prime Factorization Method, follow these steps:</p>

18 <p>To find the GCF of 16 and 100 using the Prime Factorization Method, follow these steps:</p>

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

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

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

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

22 <p>Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52</p>

21 <p>Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52</p>

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

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

24 <p>The common prime factors are: 2 x 2 = 22</p>

23 <p>The common prime factors are: 2 x 2 = 22</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 22 = 4.</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 22 = 4.</p>

26 <p>The Greatest Common Factor of 16 and 100 is 4.</p>

25 <p>The Greatest Common Factor of 16 and 100 is 4.</p>

27 <h2>GCF of 16 and 100 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 16 and 100 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 16 and 100 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 16 and 100 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 100 by 16 100 ÷ 16 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 100 - (16×6) = 4 The remainder is 4, not zero, so continue the process</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 100 by 16 100 ÷ 16 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 100 - (16×6) = 4 The remainder is 4, not zero, so continue the process</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (4) Divide 16 by 4 16 ÷ 4 = 4 (quotient), remainder = 16 - (4×4) = 0</p>

29 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (4) Divide 16 by 4 16 ÷ 4 = 4 (quotient), remainder = 16 - (4×4) = 0</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 100 is 4.</p>

30 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 100 is 4.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 100</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 100</h2>

33 <p>Finding GCF of 16 and 100 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

32 <p>Finding GCF of 16 and 100 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>A gardener has 16 rose bushes and 100 tulip bulbs. She wants to plant them in rows with an equal number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?</p>

34 <p>A gardener has 16 rose bushes and 100 tulip bulbs. She wants to plant them in rows with an equal number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?</p>

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

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

37 <p>We should find the GCF of 16 and 100 GCF of 16 and 100 22 = 4.</p>

36 <p>We should find the GCF of 16 and 100 GCF of 16 and 100 22 = 4.</p>

38 <p>There are 4 equal rows 16 ÷ 4 = 4 100 ÷ 4 = 25</p>

37 <p>There are 4 equal rows 16 ÷ 4 = 4 100 ÷ 4 = 25</p>

39 <p>There will be 4 rows, and each row gets 4 rose bushes and 25 tulip bulbs.</p>

38 <p>There will be 4 rows, and each row gets 4 rose bushes and 25 tulip bulbs.</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>As the GCF of 16 and 100 is 4, the gardener can make 4 rows. Now divide 16 and 100 by 4. Each row gets 4 rose bushes and 25 tulip bulbs.</p>

40 <p>As the GCF of 16 and 100 is 4, the gardener can make 4 rows. Now divide 16 and 100 by 4. Each row gets 4 rose bushes and 25 tulip bulbs.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>A baker has 16 chocolate muffins and 100 vanilla muffins. She wants to arrange them on trays with the same number of muffins on each tray, using the largest possible number of muffins per tray. How many muffins will be on each tray?</p>

43 <p>A baker has 16 chocolate muffins and 100 vanilla muffins. She wants to arrange them on trays with the same number of muffins on each tray, using the largest possible number of muffins per tray. How many muffins will be on each tray?</p>

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

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

46 <p>GCF of 16 and 100 22 = 4. So each tray will have 4 muffins.</p>

45 <p>GCF of 16 and 100 22 = 4. So each tray will have 4 muffins.</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>There are 16 chocolate and 100 vanilla muffins. To find the total number of muffins on each tray, we should find the GCF of 16 and 100. There will be 4 muffins on each tray.</p>

47 <p>There are 16 chocolate and 100 vanilla muffins. To find the total number of muffins on each tray, we should find the GCF of 16 and 100. There will be 4 muffins on each tray.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

49 <h3>Problem 3</h3>

51 <p>A tailor has 16 meters of silk fabric and 100 meters of cotton 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>

50 <p>A tailor has 16 meters of silk fabric and 100 meters of cotton 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>Okay, lets begin</p>

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

53 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 100 The GCF of 16 and 100 22 = 4. The fabric is 4 meters long.</p>

52 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 100 The GCF of 16 and 100 22 = 4. The fabric is 4 meters long.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 16 and 100, which is 4. The length of each piece of fabric will be 4 meters.</p>

54 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 16 and 100, which is 4. The length of each piece of fabric will be 4 meters.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

56 <h3>Problem 4</h3>

58 <p>A carpenter has two wooden planks, one 16 cm long and the other 100 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>

57 <p>A carpenter has two wooden planks, one 16 cm long and the other 100 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>

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

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

60 <p>The carpenter needs the longest piece of wood GCF of 16 and 100 22 = 4. The longest length of each piece is 4 cm.</p>

59 <p>The carpenter needs the longest piece of wood GCF of 16 and 100 22 = 4. The longest length of each piece is 4 cm.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 100 cm, respectively. We have to find the GCF of 16 and 100, which is 4 cm. The longest length of each piece is 4 cm.</p>

61 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 100 cm, respectively. We have to find the GCF of 16 and 100, which is 4 cm. The longest length of each piece is 4 cm.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>If the GCF of 16 and ‘b’ is 4, and the LCM is 400. Find ‘b’.</p>

64 <p>If the GCF of 16 and ‘b’ is 4, and the LCM is 400. Find ‘b’.</p>

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

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

67 <p>The value of ‘b’ is 100.</p>

66 <p>The value of ‘b’ is 100.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

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

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

70 <p>4 × 400 = 16 × b</p>

69 <p>4 × 400 = 16 × b</p>

71 <p>1600 = 16b</p>

70 <p>1600 = 16b</p>

72 <p>b = 1600 ÷ 16 = 100</p>

71 <p>b = 1600 ÷ 16 = 100</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h2>FAQs on the Greatest Common Factor of 16 and 100</h2>

73 <h2>FAQs on the Greatest Common Factor of 16 and 100</h2>

75 <h3>1.What is the LCM of 16 and 100?</h3>

74 <h3>1.What is the LCM of 16 and 100?</h3>

76 <p>The LCM of 16 and 100 is 400.</p>

75 <p>The LCM of 16 and 100 is 400.</p>

77 <h3>2.Is 16 divisible by 2?</h3>

76 <h3>2.Is 16 divisible by 2?</h3>

78 <p>Yes, 16 is divisible by 2 because it is an even number.</p>

77 <p>Yes, 16 is divisible by 2 because it is an even number.</p>

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

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

80 <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>

79 <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>

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

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

82 <p>The prime factorization of 100 is 2^2 x 5^2.</p>

81 <p>The prime factorization of 100 is 2^2 x 5^2.</p>

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

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

84 <p>No, 16 and 100 are not prime numbers because both of them have more than two factors.</p>

83 <p>No, 16 and 100 are not prime numbers because both of them have more than two factors.</p>

85 <h2>Important Glossaries for GCF of 16 and 100</h2>

84 <h2>Important Glossaries for GCF of 16 and 100</h2>

86 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.</li>

85 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.</li>

87 </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>

86 </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>

88 </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 18 are 2 and 3.</li>

87 </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 18 are 2 and 3.</li>

89 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.</li>

88 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.</li>

90 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 100 is 400.</li>

89 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 100 is 400.</li>

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

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

92 <p>▶</p>

91 <p>▶</p>

93 <h2>Hiralee Lalitkumar Makwana</h2>

92 <h2>Hiralee Lalitkumar Makwana</h2>

94 <h3>About the Author</h3>

93 <h3>About the Author</h3>

95 <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>

94 <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>

96 <h3>Fun Fact</h3>

95 <h3>Fun Fact</h3>

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

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