101 LearnersLast updated on August 1st, 2025
GCF of 48 and 64
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 48 and 64.
What is the GCF of 48 and 64?
The greatest common factor of 48 and 64 is 16. The largest divisor of two or more numbers is called the GCF of the numbers. 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 48 and 64?
To find the GCF of 48 and 64, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 48 and 64 by Using Listing of factors
Steps to find the GCF of 48 and 64 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors of them Common factors of 48 and 64: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor
The largest factor that both numbers have is 16.
The GCF of 48 and 64 is 16.
GCF of 48 and 64 Using Prime Factorization
To find the GCF of 48 and 64 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3
Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 2 x 2 = 2^4
Step 3: Multiply the common prime factors 2^4 = 16.
The Greatest Common Factor of 48 and 64 is 16.
GCF of 48 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 48 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 64 by 48 64 ÷ 48 = 1 (quotient),
The remainder is calculated as 64 − (48×1) = 16
The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (48) by the previous remainder (16)
Divide 48 by 16 48 ÷ 16 = 3 (quotient), remainder = 48 − (16×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 48 and 64 is 16.
Common Mistakes and How to Avoid Them in GCF of 48 and 64
Finding GCF of 48 and 64 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 48, 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 between 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 48 and 64 Examples
Problem 1
A gardener has 48 rose plants and 64 sunflower plants. She wants to group them into equal sets, with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 48 and 64 GCF of 48 and 64 2^4 = 16.
There are 16 equal groups 48 ÷ 16 = 3 64 ÷ 16 = 4
There will be 16 groups, and each group gets 3 rose plants and 4 sunflower plants.
Explanation
As the GCF of 48 and 64 is 16, the gardener can make 16 groups. Now divide 48 and 64 by 16. Each group gets 3 rose plants and 4 sunflower plants.
Problem 2
A bakery has 48 chocolate cupcakes and 64 vanilla cupcakes. They want to arrange them in trays with the same number of cupcakes on each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be on each tray?
GCF of 48 and 64 2^4 = 16.
So each tray will have 16 cupcakes.
Explanation
There are 48 chocolate and 64 vanilla cupcakes. To find the total number of cupcakes on each tray, we should find the GCF of 48 and 64. There will be 16 cupcakes on each tray.
Problem 3
A ribbon factory has 48 meters of green ribbon and 64 meters of blue ribbon. They want to cut both ribbons 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 48 and 64
The GCF of 48 and 64 2^4 = 16.
The ribbon is 16 meters long.
Explanation
For calculating the longest length of the ribbon first, we need to calculate the GCF of 48 and 64, which is 16. The length of each piece of the ribbon will be 16 meters.
Problem 4
A carpenter has two wooden planks, one 48 cm long and the other 64 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 48 and 64 2^4 = 16.
The longest length of each piece is 16 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 48 cm and 64 cm, respectively. We have to find the GCF of 48 and 64, which is 16 cm. The longest length of each piece is 16 cm.
Problem 5
If the GCF of 48 and ‘b’ is 16, and the LCM is 192. Find ‘b’.
The value of ‘b’ is 64.
Explanation
GCF x LCM = product of the numbers 16 × 192 = 48 × b
3072 = 48b
b = 3072 ÷ 48 = 64
FAQs on the Greatest Common Factor of 48 and 64
1.What is the LCM of 48 and 64?
2.Is 64 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 48 and 64 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 48 and 64?
7.What are some fun ways kids in Vietnam can practice GCF of 48 and 64 with numbers?
8.What role do numbers and GCF of 48 and 64 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 48 and 64 skills?
Important Glossaries for GCF of 48 and 64
- 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 the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 64 is 192.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 48 and 64 is 16, as it is their largest common factor that divides the numbers completely.
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.
