# Greatest Common Factor of 40 and 52

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 40, 52 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 40 and 52 is 4.

GCF(40,52) = 4

## GCF of 40 and 52

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

GCF of:
and

### Greatest Common Factor of 40 and 52 by Prime factorization method

Prime Factorization of 40

 2 40 2 20 2 10 5 5 1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

Prime Factorization of 52

 2 52 2 26 13 13 1

Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:

52 = 22×131

∴ So by taking common prime factors GCF of 40 and 52 is 4

### Greatest Common Factor of 40 and 52 by matching factors method

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1,2,4,13,26,52

Greatest Common Factor

We found the factors and prime factorization of 40 and 52. The biggest common factor number is the GCF number.
So the greatest common factor 40 and 52 is 4.

Also check out the Least Common Multiple of 40 and 52

### Properties of GCF 40 and 52

(i) The GCF of 40 and 52 is associative

GCF of 40 and 52 = GCF of 52 and 40

### Frequently Asked Questions on GCF of 40 and 52

1. What is the GCF of 40 and 52?

Answer: GCF of 40 and 52 is 4.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

3. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

4. How to Find the GCF of 40 and 52?

Greatest Common Factor of 40 and 52 = 4

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 52

52 = 2 x 2 x 13

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 40 and 52 is 4