Greatest Common Factor of 514 and 518

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 514, 518 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 514 and 518 is 2.

GCF(514,518) = 2

GCF of 514 and 518

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

GCF of:
and

Greatest Common Factor of 514 and 518

GCF of 514 and 518 is 2

Prime Factorization of 514


2 514
257 257
1

Prime factors of 514 are 2,257. Prime factorization of 514 in exponential form is:

514 = 21×2571

Prime Factorization of 518


2 518
7 259
37 37
1

Prime factors of 518 are 2,7,37. Prime factorization of 518 in exponential form is:

518 = 21×71×371

∴ So by taking common prime factors GCF of 514 and 518 is 2

Greatest Common Factor of 514 and 518 by matching factors method

Factors of 514

List of positive integer factors of 514 that divides 514 without a remainder.

1,2,257,514

Factors of 518

List of positive integer factors of 518 that divides 518 without a remainder.

1,2,7,14,37,74,259,518

Greatest Common Factor

We found the factors and prime factorization of 514 and 518. The biggest common factor number is the GCF number.
So the greatest common factor 514 and 518 is 2.

Also check out the Least Common Multiple of 514 and 518

Properties of GCF 514 and 518

(i) The GCF of 514 and 518 is associative

GCF of 514 and 518 = GCF of 518 and 514

Related Greatest Common Factor of 514

Related Greatest Common Factor of 518

Frequently Asked Questions on GCF of 514 and 518

1. What is the GCF of 514 and 518?

Answer: GCF of 514 and 518 is 2.

2. What are the Factors of 514?

Answer: Factors of 514 are 1, 2, 257, 514. There are 4 integers that are factors of 514. The greatest factor of 514 is 514.

3. What are the Factors of 518?

Answer: Factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518. There are 8 integers that are factors of 518. The greatest factor of 518 is 518.

4. How to Find the GCF of 514 and 518?

Answer:

Greatest Common Factor of 514 and 518 = 2

Step 1: Find the prime factorization of 514

514 = 2 x 257

Step 2: Find the prime factorization of 518

518 = 2 x 7 x 37

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 514 and 518 is 2