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
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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
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
(i) The GCF of 120 and 128 is associative
GCF of 120 and 128 = GCF of 128 and 120
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