Greatest Common Factor of 514 and 520

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

Greatest common factor (GCF) of 514 and 520 is 2.

GCF(514,520) = 2

GCF of 514 and 520

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

GCF of:
and

Greatest Common Factor of 514 and 520

GCF of 514 and 520 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 520


2 520
2 260
2 130
5 65
13 13
1

Prime factors of 520 are 2,5,13. Prime factorization of 520 in exponential form is:

520 = 23×51×131

∴ So by taking common prime factors GCF of 514 and 520 is 2

Greatest Common Factor of 514 and 520 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 520

List of positive integer factors of 520 that divides 520 without a remainder.

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Greatest Common Factor

We found the factors and prime factorization of 514 and 520. The biggest common factor number is the GCF number.
So the greatest common factor 514 and 520 is 2.

Also check out the Least Common Multiple of 514 and 520

Properties of GCF 514 and 520

(i) The GCF of 514 and 520 is associative

GCF of 514 and 520 = GCF of 520 and 514

Related Greatest Common Factor of 514

Related Greatest Common Factor of 520

Frequently Asked Questions on GCF of 514 and 520

1. What is the GCF of 514 and 520?

Answer: GCF of 514 and 520 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 520?

Answer: Factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520. There are 16 integers that are factors of 520. The greatest factor of 520 is 520.

4. How to Find the GCF of 514 and 520?

Answer:

Greatest Common Factor of 514 and 520 = 2

Step 1: Find the prime factorization of 514

514 = 2 x 257

Step 2: Find the prime factorization of 520

520 = 2 x 2 x 2 x 5 x 13

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 520 is 2