Greatest Common Factor of 506 and 510

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

Greatest common factor (GCF) of 506 and 510 is 2.

GCF(506,510) = 2

GCF of 506 and 510

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

GCF of:
and

Greatest Common Factor of 506 and 510

GCF of 506 and 510 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 510


2 510
3 255
5 85
17 17
1

Prime factors of 510 are 2,3,5,17. Prime factorization of 510 in exponential form is:

510 = 21×31×51×171

∴ So by taking common prime factors GCF of 506 and 510 is 2

Greatest Common Factor of 506 and 510 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 510

List of positive integer factors of 510 that divides 510 without a remainder.

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Greatest Common Factor

We found the factors and prime factorization of 506 and 510. The biggest common factor number is the GCF number.
So the greatest common factor 506 and 510 is 2.

Also check out the Least Common Multiple of 506 and 510

Properties of GCF 506 and 510

(i) The GCF of 506 and 510 is associative

GCF of 506 and 510 = GCF of 510 and 506

Related Greatest Common Factor of 506

Related Greatest Common Factor of 510

Frequently Asked Questions on GCF of 506 and 510

1. What is the GCF of 506 and 510?

Answer: GCF of 506 and 510 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 510?

Answer: Factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. There are 16 integers that are factors of 510. The greatest factor of 510 is 510.

4. How to Find the GCF of 506 and 510?

Answer:

Greatest Common Factor of 506 and 510 = 2

Step 1: Find the prime factorization of 506

506 = 2 x 11 x 23

Step 2: Find the prime factorization of 510

510 = 2 x 3 x 5 x 17

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 510 is 2