Greatest Common Factor of 506 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 506, 514 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 506 and 514 is 2.

GCF(506,514) = 2

GCF of 506 and 514

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

GCF of:
and

Greatest Common Factor of 506 and 514

GCF of 506 and 514 is 2

Prime Factorization of 506


2 506
11 253
23 23
1

Prime factors of 506 are 2,11,23. Prime factorization of 506 in exponential form is:

506 = 21×111×231

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 506 and 514 is 2

Greatest Common Factor of 506 and 514 by matching factors method

Factors of 506

List of positive integer factors of 506 that divides 506 without a remainder.

1,2,11,22,23,46,253,506

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 506 and 514. The biggest common factor number is the GCF number.
So the greatest common factor 506 and 514 is 2.

Also check out the Least Common Multiple of 506 and 514

Properties of GCF 506 and 514

(i) The GCF of 506 and 514 is associative

GCF of 506 and 514 = GCF of 514 and 506

Related Greatest Common Factor of 506

Related Greatest Common Factor of 514

Frequently Asked Questions on GCF of 506 and 514

1. What is the GCF of 506 and 514?

Answer: GCF of 506 and 514 is 2.

2. What are the Factors of 506?

Answer: Factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506. There are 8 integers that are factors of 506. The greatest factor of 506 is 506.

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 506 and 514?

Answer:

Greatest Common Factor of 506 and 514 = 2

Step 1: Find the prime factorization of 506

506 = 2 x 11 x 23

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 506 and 514 is 2