Greatest Common Factor of 516 and 522

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 516, 522 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 516 and 522 is 6.

GCF(516,522) = 6

GCF of 516 and 522

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

GCF of:
and

Greatest Common Factor of 516 and 522

GCF of 516 and 522 is 6

Prime Factorization of 516


2 516
2 258
3 129
43 43
1

Prime factors of 516 are 2,3,43. Prime factorization of 516 in exponential form is:

516 = 22×31×431

Prime Factorization of 522


2 522
3 261
3 87
29 29
1

Prime factors of 522 are 2,3,29. Prime factorization of 522 in exponential form is:

522 = 21×32×291

∴ So by taking common prime factors GCF of 516 and 522 is 6

Greatest Common Factor of 516 and 522 by matching factors method

Factors of 516

List of positive integer factors of 516 that divides 516 without a remainder.

1,2,3,4,6,12,43,86,129,172,258,516

Factors of 522

List of positive integer factors of 522 that divides 522 without a remainder.

1,2,3,6,9,18,29,58,87,174,261,522

Greatest Common Factor

We found the factors and prime factorization of 516 and 522. The biggest common factor number is the GCF number.
So the greatest common factor 516 and 522 is 6.

Also check out the Least Common Multiple of 516 and 522

Properties of GCF 516 and 522

(i) The GCF of 516 and 522 is associative

GCF of 516 and 522 = GCF of 522 and 516

Related Greatest Common Factor of 516

Related Greatest Common Factor of 522

Frequently Asked Questions on GCF of 516 and 522

1. What is the GCF of 516 and 522?

Answer: GCF of 516 and 522 is 6.

2. What are the Factors of 516?

Answer: Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516. There are 12 integers that are factors of 516. The greatest factor of 516 is 516.

3. What are the Factors of 522?

Answer: Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522. There are 12 integers that are factors of 522. The greatest factor of 522 is 522.

4. How to Find the GCF of 516 and 522?

Answer:

Greatest Common Factor of 516 and 522 = 6

Step 1: Find the prime factorization of 516

516 = 2 x 2 x 3 x 43

Step 2: Find the prime factorization of 522

522 = 2 x 3 x 3 x 29

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 516 and 522 is 6