Greatest Common Factor of 513 and 516

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 513, 516 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 513 and 516 is 3.

GCF(513,516) = 3

GCF of 513 and 516

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

GCF of:
and

Greatest Common Factor of 513 and 516

GCF of 513 and 516 is 3

Prime Factorization of 513


3 513
3 171
3 57
19 19
1

Prime factors of 513 are 3,19. Prime factorization of 513 in exponential form is:

513 = 33×191

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

∴ So by taking common prime factors GCF of 513 and 516 is 3

Greatest Common Factor of 513 and 516 by matching factors method

Factors of 513

List of positive integer factors of 513 that divides 513 without a remainder.

1,3,9,19,27,57,171,513

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

Greatest Common Factor

We found the factors and prime factorization of 513 and 516. The biggest common factor number is the GCF number.
So the greatest common factor 513 and 516 is 3.

Also check out the Least Common Multiple of 513 and 516

Properties of GCF 513 and 516

(i) The GCF of 513 and 516 is associative

GCF of 513 and 516 = GCF of 516 and 513

Related Greatest Common Factor of 513

Related Greatest Common Factor of 516

Frequently Asked Questions on GCF of 513 and 516

1. What is the GCF of 513 and 516?

Answer: GCF of 513 and 516 is 3.

2. What are the Factors of 513?

Answer: Factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513. There are 8 integers that are factors of 513. The greatest factor of 513 is 513.

3. 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.

4. How to Find the GCF of 513 and 516?

Answer:

Greatest Common Factor of 513 and 516 = 3

Step 1: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 516

516 = 2 x 2 x 3 x 43

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

GCF = 3

Step 4: Therefore, the greatest common factor of 513 and 516 is 3