Greatest Common Factor of 513 and 519

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

Greatest common factor (GCF) of 513 and 519 is 3.

GCF(513,519) = 3

GCF of 513 and 519

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

GCF of:
and

Greatest Common Factor of 513 and 519

GCF of 513 and 519 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 519


3 519
173 173
1

Prime factors of 519 are 3,173. Prime factorization of 519 in exponential form is:

519 = 31×1731

∴ So by taking common prime factors GCF of 513 and 519 is 3

Greatest Common Factor of 513 and 519 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 519

List of positive integer factors of 519 that divides 519 without a remainder.

1,3,173,519

Greatest Common Factor

We found the factors and prime factorization of 513 and 519. The biggest common factor number is the GCF number.
So the greatest common factor 513 and 519 is 3.

Also check out the Least Common Multiple of 513 and 519

Properties of GCF 513 and 519

(i) The GCF of 513 and 519 is associative

GCF of 513 and 519 = GCF of 519 and 513

Related Greatest Common Factor of 513

Related Greatest Common Factor of 519

Frequently Asked Questions on GCF of 513 and 519

1. What is the GCF of 513 and 519?

Answer: GCF of 513 and 519 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 519?

Answer: Factors of 519 are 1, 3, 173, 519. There are 4 integers that are factors of 519. The greatest factor of 519 is 519.

4. How to Find the GCF of 513 and 519?

Answer:

Greatest Common Factor of 513 and 519 = 3

Step 1: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 519

519 = 3 x 173

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 519 is 3