Greatest Common Factor of 514 and 522

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

Greatest common factor (GCF) of 514 and 522 is 2.

GCF(514,522) = 2

GCF of 514 and 522

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

GCF of:
and

Greatest Common Factor of 514 and 522

GCF of 514 and 522 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 522


2 522
3 261
3 87
29 29
1

Prime factors of 522 are 2,3,29. Prime factorization of 522 in exponential form is:

522 = 21×32×291

∴ So by taking common prime factors GCF of 514 and 522 is 2

Greatest Common Factor of 514 and 522 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 522

List of positive integer factors of 522 that divides 522 without a remainder.

1,2,3,6,9,18,29,58,87,174,261,522

Greatest Common Factor

We found the factors and prime factorization of 514 and 522. The biggest common factor number is the GCF number.
So the greatest common factor 514 and 522 is 2.

Also check out the Least Common Multiple of 514 and 522

Properties of GCF 514 and 522

(i) The GCF of 514 and 522 is associative

GCF of 514 and 522 = GCF of 522 and 514

Related Greatest Common Factor of 514

Related Greatest Common Factor of 522

Frequently Asked Questions on GCF of 514 and 522

1. What is the GCF of 514 and 522?

Answer: GCF of 514 and 522 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 522?

Answer: Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522. There are 12 integers that are factors of 522. The greatest factor of 522 is 522.

4. How to Find the GCF of 514 and 522?

Answer:

Greatest Common Factor of 514 and 522 = 2

Step 1: Find the prime factorization of 514

514 = 2 x 257

Step 2: Find the prime factorization of 522

522 = 2 x 3 x 3 x 29

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 522 is 2