Greatest Common Factor of 120 and 125

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, 125 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 120 and 125 is 5.

GCF(120,125) = 5

GCF of 120 and 125

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

GCF of:
and

Greatest Common Factor of 120 and 125

GCF of 120 and 125 is 5

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 125


5 125
5 25
5 5
1

Prime factors of 125 are 5. Prime factorization of 125 in exponential form is:

125 = 53

∴ So by taking common prime factors GCF of 120 and 125 is 5

Greatest Common Factor of 120 and 125 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 125

List of positive integer factors of 125 that divides 125 without a remainder.

1,5,25,125

Greatest Common Factor

We found the factors and prime factorization of 120 and 125. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 125 is 5.

Also check out the Least Common Multiple of 120 and 125

Properties of GCF 120 and 125

(i) The GCF of 120 and 125 is associative

GCF of 120 and 125 = GCF of 125 and 120

Related Greatest Common Factor of 120

Related Greatest Common Factor of 125

Frequently Asked Questions on GCF of 120 and 125

1. What is the GCF of 120 and 125?

Answer: GCF of 120 and 125 is 5.

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 125?

Answer: Factors of 125 are 1, 5, 25, 125. There are 4 integers that are factors of 125. The greatest factor of 125 is 125.

4. How to Find the GCF of 120 and 125?

Answer:

Greatest Common Factor of 120 and 125 = 5

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 125

125 = 5 x 5 x 5

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

GCF = 5

Step 4: Therefore, the greatest common factor of 120 and 125 is 5