Greatest Common Factor of 508 and 514

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 508, 514 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 508 and 514 is 2.

GCF(508,514) = 2

GCF of 508 and 514

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

GCF of:
and

Greatest Common Factor of 508 and 514

GCF of 508 and 514 is 2

Prime Factorization of 508


2 508
2 254
127 127
1

Prime factors of 508 are 2,127. Prime factorization of 508 in exponential form is:

508 = 22×1271

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

∴ So by taking common prime factors GCF of 508 and 514 is 2

Greatest Common Factor of 508 and 514 by matching factors method

Factors of 508

List of positive integer factors of 508 that divides 508 without a remainder.

1,2,4,127,254,508

Factors of 514

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

1,2,257,514

Greatest Common Factor

We found the factors and prime factorization of 508 and 514. The biggest common factor number is the GCF number.
So the greatest common factor 508 and 514 is 2.

Also check out the Least Common Multiple of 508 and 514

Properties of GCF 508 and 514

(i) The GCF of 508 and 514 is associative

GCF of 508 and 514 = GCF of 514 and 508

Related Greatest Common Factor of 508

Related Greatest Common Factor of 514

Frequently Asked Questions on GCF of 508 and 514

1. What is the GCF of 508 and 514?

Answer: GCF of 508 and 514 is 2.

2. What are the Factors of 508?

Answer: Factors of 508 are 1, 2, 4, 127, 254, 508. There are 6 integers that are factors of 508. The greatest factor of 508 is 508.

3. 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.

4. How to Find the GCF of 508 and 514?

Answer:

Greatest Common Factor of 508 and 514 = 2

Step 1: Find the prime factorization of 508

508 = 2 x 2 x 127

Step 2: Find the prime factorization of 514

514 = 2 x 257

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 508 and 514 is 2