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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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 16 and 48.</p>

4 <h2>What is the GCF of 16 and 48?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>16 and 48 is 16. 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 48?</h2>

7 <p>To find the GCF of 16 and 48, a few methods are described below:</p>

8 <ul><li>Listing Factors </li>

9 <li>Prime Factorization </li>

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

11 </ul><h3>GCF of 16 and 48 by Using Listing of factors</h3>

12 <p>Steps to find the GCF of 16 and 48 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 16 = 1, 2, 4, 8, 16.</p>

15 <p>Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 16 and 48: 1, 2, 4, 8, 16.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 16. The GCF of 16 and 48 is 16.</p>

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20 <h3>GCF of 16 and 48 Using Prime Factorization</h3>

19 <h3>GCF of 16 and 48 Using Prime Factorization</h3>

21 <p>To find the GCF of 16 and 48 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 16 and 48 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 16: 16 = 2 × 2 × 2 × 2 = 24</p>

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

24 <p>Prime Factors of 48: 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3</p>

23 <p>Prime Factors of 48: 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 × 2 = 24</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 × 2 = 24</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 24 = 16. The Greatest Common Factor of 16 and 48 is 16.</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 24 = 16. The Greatest Common Factor of 16 and 48 is 16.</p>

27 <h3>GCF of 16 and 48 Using Division Method or Euclidean Algorithm Method</h3>

26 <h3>GCF of 16 and 48 Using Division Method or Euclidean Algorithm Method</h3>

28 <p>Find the GCF of 16 and 48 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 16 and 48 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 48 by 16 48 ÷ 16 = 3 (<a>quotient</a>).</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 48 by 16 48 ÷ 16 = 3 (<a>quotient</a>).</p>

30 <p>The<a>remainder</a>is calculated as 48 - (16×3) = 0.</p>

29 <p>The<a>remainder</a>is calculated as 48 - (16×3) = 0.</p>

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

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

32 <p>The GCF of 16 and 48 is 16.</p>

31 <p>The GCF of 16 and 48 is 16.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 48</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 16 and 48</h2>

34 <p>Finding GCF of 16 and 48 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <p>Finding GCF of 16 and 48 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A chef has 16 apples and 48 oranges. He wants to arrange them into equal baskets, with the largest number of fruits in each basket. How many fruits will be in each basket?</p>

35 <p>A chef has 16 apples and 48 oranges. He wants to arrange them into equal baskets, with the largest number of fruits in each basket. How many fruits will be in each basket?</p>

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

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

38 <p>We should find the GCF of 16 and 48</p>

37 <p>We should find the GCF of 16 and 48</p>

39 <p>GCF of 16 and 48 24 = 16.</p>

38 <p>GCF of 16 and 48 24 = 16.</p>

40 <p>There are 16 equal baskets 16 ÷ 16 = 1 48 ÷ 16 = 3</p>

39 <p>There are 16 equal baskets 16 ÷ 16 = 1 48 ÷ 16 = 3</p>

41 <p>There will be 16 baskets, and each basket gets 1 apple and 3 oranges.</p>

40 <p>There will be 16 baskets, and each basket gets 1 apple and 3 oranges.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>As the GCF of 16 and 48 is 16, the chef can make 16 baskets.</p>

42 <p>As the GCF of 16 and 48 is 16, the chef can make 16 baskets.</p>

44 <p>Now divide 16 and 48 by 16.</p>

43 <p>Now divide 16 and 48 by 16.</p>

45 <p>Each basket gets 1 apple and 3 oranges.</p>

44 <p>Each basket gets 1 apple and 3 oranges.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 2</h3>

46 <h3>Problem 2</h3>

48 <p>A florist has 16 roses and 48 lilies. She wants to arrange them in bouquets with the same number of flowers in each bouquet, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?</p>

47 <p>A florist has 16 roses and 48 lilies. She wants to arrange them in bouquets with the same number of flowers in each bouquet, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?</p>

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

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

50 <p>GCF of 16 and 48 24 = 16.</p>

49 <p>GCF of 16 and 48 24 = 16.</p>

51 <p>So each bouquet will have 16 flowers.</p>

50 <p>So each bouquet will have 16 flowers.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>There are 16 roses and 48 lilies.</p>

52 <p>There are 16 roses and 48 lilies.</p>

54 <p>To find the total number of flowers in each bouquet, we should find the GCF of 16 and 48.</p>

53 <p>To find the total number of flowers in each bouquet, we should find the GCF of 16 and 48.</p>

55 <p>There will be 16 flowers in each bouquet.</p>

54 <p>There will be 16 flowers in each bouquet.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>A farmer has 16 meters of red fencing and 48 meters of green fencing. He wants to cut both fences into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

57 <p>A farmer has 16 meters of red fencing and 48 meters of green fencing. He wants to cut both fences 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 48 The GCF of 16 and 48 24 = 16.</p>

59 <p>For calculating the longest equal length, we have to calculate the GCF of 16 and 48 The GCF of 16 and 48 24 = 16.</p>

61 <p>The fence is 16 meters long.</p>

60 <p>The fence is 16 meters long.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>For calculating the longest length of the fence, first, we need to calculate the GCF of 16 and 48, which is 16. The length of each piece of the fence will be 16 meters.</p>

62 <p>For calculating the longest length of the fence, first, we need to calculate the GCF of 16 and 48, which is 16. The length of each piece of the fence will be 16 meters.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

64 <h3>Problem 4</h3>

66 <p>A carpenter has two wooden planks, one 16 cm long and the other 48 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>

65 <p>A carpenter has two wooden planks, one 16 cm long and the other 48 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>Okay, lets begin</p>

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

68 <p>The carpenter needs the longest piece of wood GCF of 16 and 48 24 = 16. The longest length of each piece is 16 cm.</p>

67 <p>The carpenter needs the longest piece of wood GCF of 16 and 48 24 = 16. The longest length of each piece is 16 cm.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 48 cm, respectively. We have to find the GCF of 16 and 48, which is 16 cm. The longest length of each piece is 16 cm.</p>

69 <p>To find the longest length of each piece of the two wooden planks, 16 cm and 48 cm, respectively. We have to find the GCF of 16 and 48, which is 16 cm. The longest length of each piece is 16 cm.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 5</h3>

71 <h3>Problem 5</h3>

73 <p>If the GCF of 16 and ‘a’ is 16, and the LCM is 48. Find ‘a’.</p>

72 <p>If the GCF of 16 and ‘a’ is 16, and the LCM is 48. Find ‘a’.</p>

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

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

75 <p>The value of ‘a’ is 48.</p>

74 <p>The value of ‘a’ is 48.</p>

76 <h3>Explanation</h3>

75 <h3>Explanation</h3>

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

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

78 <p>16 × 48 = 16 × a</p>

77 <p>16 × 48 = 16 × a</p>

79 <p>768 = 16a</p>

78 <p>768 = 16a</p>

80 <p>a = 768 ÷ 16 = 48</p>

79 <p>a = 768 ÷ 16 = 48</p>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h2>FAQs on the Greatest Common Factor of 16 and 48</h2>

81 <h2>FAQs on the Greatest Common Factor of 16 and 48</h2>

83 <h3>1.What is the LCM of 16 and 48?</h3>

82 <h3>1.What is the LCM of 16 and 48?</h3>

84 <p>The LCM of 16 and 48 is 48.</p>

83 <p>The LCM of 16 and 48 is 48.</p>

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

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

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

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

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

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

88 <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>

87 <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>

89 <h3>4.What is the prime factorization of 48?</h3>

88 <h3>4.What is the prime factorization of 48?</h3>

90 <p>The prime factorization of 48 is 24 × 3.</p>

89 <p>The prime factorization of 48 is 24 × 3.</p>

91 <h3>5.Are 16 and 48 prime numbers?</h3>

90 <h3>5.Are 16 and 48 prime numbers?</h3>

92 <p>No, 16 and 48 are not prime numbers because both of them have more than two factors.</p>

91 <p>No, 16 and 48 are not prime numbers because both of them have more than two factors.</p>

93 <h2>Important Glossaries for GCF of 16 and 48</h2>

92 <h2>Important Glossaries for GCF of 16 and 48</h2>

94 <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>

93 <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>

95 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.</li>

94 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.</li>

96 </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 48 are 2 and 3.</li>

95 </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 48 are 2 and 3.</li>

97 </ul><ul><li><strong>Remainder:</strong>The value left after division when a number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

96 </ul><ul><li><strong>Remainder:</strong>The value left after division when a number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

98 </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 48 is 48.</li>

97 </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 48 is 48.</li>

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

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

100 <p>▶</p>

99 <p>▶</p>

101 <h2>Hiralee Lalitkumar Makwana</h2>

100 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h3>About the Author</h3>

101 <h3>About the Author</h3>

103 <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>

102 <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>

104 <h3>Fun Fact</h3>

103 <h3>Fun Fact</h3>

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

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