Greatest Common Factor of 10 and 25

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 10, 25 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 10 and 25 is 5.

GCF(10,25) = 5

GCF of 10 and 25

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

GCF of:
and

Greatest Common Factor of 10 and 25

GCF of 10 and 25 is 5

Prime Factorization of 10


2 10
5 5
1

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 21×51

Prime Factorization of 25


5 25
5 5
1

Prime factors of 25 are 5. Prime factorization of 25 in exponential form is:

25 = 52

∴ So by taking common prime factors GCF of 10 and 25 is 5

Greatest Common Factor of 10 and 25 by matching factors method

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Factors of 25

List of positive integer factors of 25 that divides 25 without a remainder.

1,5,25

Greatest Common Factor

We found the factors and prime factorization of 10 and 25. The biggest common factor number is the GCF number.
So the greatest common factor 10 and 25 is 5.

Also check out the Least Common Multiple of 10 and 25

Properties of GCF 10 and 25

(i) The GCF of 10 and 25 is associative

GCF of 10 and 25 = GCF of 25 and 10

Related Greatest Common Factor of 10

Related Greatest Common Factor of 25

Frequently Asked Questions on GCF of 10 and 25

1. What is the GCF of 10 and 25?

Answer: GCF of 10 and 25 is 5.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

3. What are the Factors of 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

4. How to Find the GCF of 10 and 25?

Answer:

Greatest Common Factor of 10 and 25 = 5

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 25

25 = 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 10 and 25 is 5