105 LearnersLast updated on July 28th, 2025
GCF of 16 and 48
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.
What is the GCF of 16 and 48?
The greatest common factor of 16 and 48 is 16. The largest divisor of two or more numbers 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.
How to find the GCF of 16 and 48?
To find the GCF of 16 and 48, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method or Euclidean Algorithm
GCF of 16 and 48 by Using Listing of factors
Steps to find the GCF of 16 and 48 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors of them Common factors of 16 and 48: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor The largest factor that both numbers have is 16. The GCF of 16 and 48 is 16.
GCF of 16 and 48 Using Prime Factorization
To find the GCF of 16 and 48 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 24
Prime Factors of 48: 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 × 2 = 24
Step 3: Multiply the common prime factors 24 = 16. The Greatest Common Factor of 16 and 48 is 16.
GCF of 16 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 48 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 48 by 16 48 ÷ 16 = 3 (quotient).
The remainder is calculated as 48 − (16×3) = 0.
The remainder is zero, so the divisor will become the GCF.
The GCF of 16 and 48 is 16.
Common Mistakes and How to Avoid Them in GCF of 16 and 48
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.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 16, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 16 and 48 Examples
Problem 1
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?
We should find the GCF of 16 and 48
GCF of 16 and 48 24 = 16.
There are 16 equal baskets 16 ÷ 16 = 1 48 ÷ 16 = 3
There will be 16 baskets, and each basket gets 1 apple and 3 oranges.
Explanation
As the GCF of 16 and 48 is 16, the chef can make 16 baskets.
Now divide 16 and 48 by 16.
Each basket gets 1 apple and 3 oranges.
Problem 2
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?
GCF of 16 and 48 24 = 16.
So each bouquet will have 16 flowers.
Explanation
There are 16 roses and 48 lilies.
To find the total number of flowers in each bouquet, we should find the GCF of 16 and 48.
There will be 16 flowers in each bouquet.
Problem 3
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?
For calculating the longest equal length, we have to calculate the GCF of 16 and 48 The GCF of 16 and 48 24 = 16.
The fence is 16 meters long.
Explanation
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.
Problem 4
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?
The carpenter needs the longest piece of wood GCF of 16 and 48 24 = 16. The longest length of each piece is 16 cm.
Explanation
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.
Problem 5
If the GCF of 16 and ‘a’ is 16, and the LCM is 48. Find ‘a’.
The value of ‘a’ is 48.
Explanation
GCF × LCM = product of the numbers
16 × 48 = 16 × a
768 = 16a
a = 768 ÷ 16 = 48
FAQs on the Greatest Common Factor of 16 and 48
1.What is the LCM of 16 and 48?
2.Is 16 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 16 and 48 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 16 and 48?
7.What are some fun ways kids in United Kingdom can practice GCF of 16 and 48 with numbers?
8.What role do numbers and GCF of 16 and 48 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 16 and 48 skills?
Important Glossaries for GCF of 16 and 48
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- Multiple: 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.
- Prime Factors: 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.
- Remainder: 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 48 is 48.
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
