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1 - <p>124 Learners</p>

1 + <p>142 Learners</p>

2 <p>Last updated on<strong>September 24, 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 16 and 33.</p>

4 <h2>What is the GCF of 16 and 33?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>16 and 33 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

7 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

8 <h2>How to find the GCF of 16 and 33?</h2>

9 <p>To find the GCF of 16 and 33, a few methods are described below -</p>

10 <ol><li>Listing Factors</li>

11 <li>Prime Factorization</li>

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

13 </ol><h2>GCF of 16 and 33 by Using Listing of factors</h2>

14 <p>Steps to find the GCF of 16 and 33 using the listing of<a>factors</a></p>

15 <p><strong>Step 1:</strong>Firstly, list the factors of each number</p>

16 <p>Factors of 16 = 1, 2, 4, 8, 16.</p>

17 <p>Factors of 33 = 1, 3, 11, 33.</p>

18 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 16 and 33: 1.</p>

19 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 1. The GCF of 16 and 33 is 1.</p>

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22 <h2>GCF of 16 and 33 Using Prime Factorization</h2>

21 <h2>GCF of 16 and 33 Using Prime Factorization</h2>

23 <p>To find the GCF of 16 and 33 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 16 and 33 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 16: 16 = 2 × 2 × 2 × 2 = 2⁴</p>

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

26 <p>Prime Factors of 33: 33 = 3 × 11</p>

25 <p>Prime Factors of 33: 33 = 3 × 11</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors There are no common prime factors.</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors There are no common prime factors.</p>

28 <p><strong>Step 3:</strong>If there are no common prime factors, the GCF is 1. The Greatest Common Factor of 16 and 33 is 1.</p>

27 <p><strong>Step 3:</strong>If there are no common prime factors, the GCF is 1. The Greatest Common Factor of 16 and 33 is 1.</p>

29 <h2>GCF of 16 and 33 Using Division Method or Euclidean Algorithm Method</h2>

28 <h2>GCF of 16 and 33 Using Division Method or Euclidean Algorithm Method</h2>

30 <p>Find the GCF of 16 and 33 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

29 <p>Find the GCF of 16 and 33 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 33 by 16 33 ÷ 16 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 33 - (16×2) = 1</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 33 by 16 33 ÷ 16 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 33 - (16×2) = 1</p>

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

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

33 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1) Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 16 - (1×16) = 0</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1) Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 16 - (1×16) = 0</p>

34 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 33 is 1.</p>

33 <p>The remainder is zero, the divisor will become the GCF. The GCF of 16 and 33 is 1.</p>

35 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 33</h2>

34 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 33</h2>

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

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

37 <h3>Problem 1</h3>

36 <h3>Problem 1</h3>

38 <p>A teacher has 16 apples and 33 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>

37 <p>A teacher has 16 apples and 33 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>

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

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

40 <p>We should find the GCF of 16 and 33 GCF of 16 and 33 is 1.</p>

39 <p>We should find the GCF of 16 and 33 GCF of 16 and 33 is 1.</p>

41 <p>There are 1 equal groups 16 ÷ 1 = 16</p>

40 <p>There are 1 equal groups 16 ÷ 1 = 16</p>

42 <p>33 ÷ 1 = 33</p>

41 <p>33 ÷ 1 = 33</p>

43 <p>There will be 1 group, and each group gets 16 apples and 33 oranges.</p>

42 <p>There will be 1 group, and each group gets 16 apples and 33 oranges.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>As the GCF of 16 and 33 is 1, the teacher can make only 1 group.</p>

44 <p>As the GCF of 16 and 33 is 1, the teacher can make only 1 group.</p>

46 <p>Now divide 16 and 33 by 1. Each group gets 16 apples and 33 oranges.</p>

45 <p>Now divide 16 and 33 by 1. Each group gets 16 apples and 33 oranges.</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

47 <h3>Problem 2</h3>

49 <p>A school has 16 red chairs and 33 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

48 <p>A school has 16 red chairs and 33 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

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

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

51 <p>GCF of 16 and 33 is 1. So each row will have 1 chair.</p>

50 <p>GCF of 16 and 33 is 1. So each row will have 1 chair.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>There are 16 red and 33 blue chairs.</p>

52 <p>There are 16 red and 33 blue chairs.</p>

54 <p>To find the total number of chairs in each row, we should find the GCF of 16 and 33.</p>

53 <p>To find the total number of chairs in each row, we should find the GCF of 16 and 33.</p>

55 <p>There will be 1 chair in each row.</p>

54 <p>There will be 1 chair in each row.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>A tailor has 16 meters of red ribbon and 33 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

57 <p>A tailor has 16 meters of red ribbon and 33 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

60 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 33</p>

59 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 33</p>

61 <p>The GCF of 16 and 33 is 1.</p>

60 <p>The GCF of 16 and 33 is 1.</p>

62 <p>The ribbon is 1 meter long.</p>

61 <p>The ribbon is 1 meter long.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 16 and 33 which is 1.</p>

63 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 16 and 33 which is 1.</p>

65 <p>The length of each piece of the ribbon will be 1 meter.</p>

64 <p>The length of each piece of the ribbon will be 1 meter.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h3>Problem 4</h3>

66 <h3>Problem 4</h3>

68 <p>A carpenter has two wooden planks, one 16 cm long and the other 33 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>

67 <p>A carpenter has two wooden planks, one 16 cm long and the other 33 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>

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

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

70 <p>The carpenter needs the longest piece of wood GCF of 16 and 33 is 1.</p>

69 <p>The carpenter needs the longest piece of wood GCF of 16 and 33 is 1.</p>

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

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

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 33 cm, respectively.</p>

72 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 33 cm, respectively.</p>

74 <p>We have to find the GCF of 16 and 33, which is 1 cm.</p>

73 <p>We have to find the GCF of 16 and 33, which is 1 cm.</p>

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

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

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h3>Problem 5</h3>

76 <h3>Problem 5</h3>

78 <p>If the GCF of 16 and ‘a’ is 1, and the LCM is 528. Find ‘a’.</p>

77 <p>If the GCF of 16 and ‘a’ is 1, and the LCM is 528. Find ‘a’.</p>

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

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

80 <p>The value of ‘a’ is 33.</p>

79 <p>The value of ‘a’ is 33.</p>

81 <h3>Explanation</h3>

80 <h3>Explanation</h3>

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

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

83 <p>1 × 528 = 16 × a</p>

82 <p>1 × 528 = 16 × a</p>

84 <p>528 = 16a</p>

83 <p>528 = 16a</p>

85 <p>a = 528 ÷ 16 = 33</p>

84 <p>a = 528 ÷ 16 = 33</p>

86 <p>Well explained 👍</p>

85 <p>Well explained 👍</p>

87 <h2>FAQs on the Greatest Common Factor of 16 and 33</h2>

86 <h2>FAQs on the Greatest Common Factor of 16 and 33</h2>

88 <h3>1.What is the LCM of 16 and 33?</h3>

87 <h3>1.What is the LCM of 16 and 33?</h3>

89 <p>The LCM of 16 and 33 is 528.</p>

88 <p>The LCM of 16 and 33 is 528.</p>

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

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

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

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

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

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

93 <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>

92 <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>

94 <h3>4.What is the prime factorization of 33?</h3>

93 <h3>4.What is the prime factorization of 33?</h3>

95 <p>The prime factorization of 33 is 3 × 11.</p>

94 <p>The prime factorization of 33 is 3 × 11.</p>

96 <h3>5.Are 16 and 33 prime numbers?</h3>

95 <h3>5.Are 16 and 33 prime numbers?</h3>

97 <p>No, 16 and 33 are not prime numbers because both of them have more than two factors.</p>

96 <p>No, 16 and 33 are not prime numbers because both of them have more than two factors.</p>

98 <h2>Important Glossaries for GCF of 16 and 33</h2>

97 <h2>Important Glossaries for GCF of 16 and 33</h2>

99 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</li>

98 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</li>

100 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.</li>

99 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.</li>

101 </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 33 are 3 and 11.</li>

100 </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 33 are 3 and 11.</li>

102 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 16, the remainder is 1 and the quotient is 2.</li>

101 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 16, the remainder is 1 and the quotient is 2.</li>

103 </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 33 is 528.</li>

102 </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 33 is 528.</li>

104 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 16 and 33 is 1, as it is their largest common factor that divides the numbers completely.</li>

103 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 16 and 33 is 1, as it is their largest common factor that divides the numbers completely.</li>

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

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

106 <p>▶</p>

105 <p>▶</p>

107 <h2>Hiralee Lalitkumar Makwana</h2>

106 <h2>Hiralee Lalitkumar Makwana</h2>

108 <h3>About the Author</h3>

107 <h3>About the Author</h3>

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>

108 <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>

110 <h3>Fun Fact</h3>

109 <h3>Fun Fact</h3>

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

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