# Greatest Common Factor of 10 and 12

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 10, 12 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 10 and 12 is 2.

GCF(10,12) = 2

## GCF of 10 and 12

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

GCF of:
and

### Greatest Common Factor of 10 and 12 by Prime factorization method

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 12

 2 12 2 6 3 3 1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

∴ So by taking common prime factors GCF of 10 and 12 is 2

### Greatest Common Factor of 10 and 12 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 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Greatest Common Factor

We found the factors and prime factorization of 10 and 12. The biggest common factor number is the GCF number.
So the greatest common factor 10 and 12 is 2.

Also check out the Least Common Multiple of 10 and 12

### Properties of GCF 10 and 12

(i) The GCF of 10 and 12 is associative

GCF of 10 and 12 = GCF of 12 and 10

### Frequently Asked Questions on GCF of 10 and 12

1. What is the GCF of 10 and 12?

Answer: GCF of 10 and 12 is 2.

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 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the GCF of 10 and 12?

Greatest Common Factor of 10 and 12 = 2

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 12

12 = 2 x 2 x 3

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

GCF = 2

Step 4: Therefore, the greatest common factor of 10 and 12 is 2