# Greatest Common Factor of 52 and 58

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 52, 58 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 52 and 58 is 2.

GCF(52,58) = 2

## GCF of 52 and 58

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

GCF of:
and

### Greatest Common Factor of 52 and 58 by Prime factorization method

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

Prime Factorization of 58

 2 58 29 29 1

Prime factors of 58 are 2,29. Prime factorization of 58 in exponential form is:

58 = 21×291

∴ So by taking common prime factors GCF of 52 and 58 is 2

### Greatest Common Factor of 52 and 58 by matching factors method

Factors of 52

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

1,2,4,13,26,52

Factors of 58

List of positive integer factors of 58 that divides 58 without a remainder.

1,2,29,58

Greatest Common Factor

We found the factors and prime factorization of 52 and 58. The biggest common factor number is the GCF number.
So the greatest common factor 52 and 58 is 2.

Also check out the Least Common Multiple of 52 and 58

### Properties of GCF 52 and 58

(i) The GCF of 52 and 58 is associative

GCF of 52 and 58 = GCF of 58 and 52

### Frequently Asked Questions on GCF of 52 and 58

1. What is the GCF of 52 and 58?

Answer: GCF of 52 and 58 is 2.

2. 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.

3. What are the Factors of 58?

Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.

4. How to Find the GCF of 52 and 58?

Answer:

Greatest Common Factor of 52 and 58 = 2

Step 1: Find the prime factorization of 52

52 = 2 x 2 x 13

Step 2: Find the prime factorization of 58

58 = 2 x 29

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 52 and 58 is 2