Greatest Common Factor of 120 and 128

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 120, 128 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 120 and 128 is 8.

GCF(120,128) = 8

GCF of 120 and 128

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 120 and 128

GCF of 120 and 128 is 8

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2,3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

Prime Factorization of 128


2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 128 are 2. Prime factorization of 128 in exponential form is:

128 = 27

∴ So by taking common prime factors GCF of 120 and 128 is 8

Greatest Common Factor of 120 and 128 by matching factors method

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Factors of 128

List of positive integer factors of 128 that divides 128 without a remainder.

1,2,4,8,16,32,64,128

Greatest Common Factor

We found the factors and prime factorization of 120 and 128. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 128 is 8.

Also check out the Least Common Multiple of 120 and 128

Properties of GCF 120 and 128

(i) The GCF of 120 and 128 is associative

GCF of 120 and 128 = GCF of 128 and 120

Related Greatest Common Factor of 120

Related Greatest Common Factor of 128

Frequently Asked Questions on GCF of 120 and 128

1. What is the GCF of 120 and 128?

Answer: GCF of 120 and 128 is 8.

2. What are the Factors of 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

3. What are the Factors of 128?

Answer: Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. There are 8 integers that are factors of 128. The greatest factor of 128 is 128.

4. How to Find the GCF of 120 and 128?

Answer:

Greatest Common Factor of 120 and 128 = 8

Step 1: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 128

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 120 and 128 is 8