Greatest Common Factor of 504 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 504, 510 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 504 and 510 is 6.

GCF(504,510) = 6

GCF of 504 and 510

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

GCF of:
and

Greatest Common Factor of 504 and 510

GCF of 504 and 510 is 6

Prime Factorization of 504


2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 504 are 2,3,7. Prime factorization of 504 in exponential form is:

504 = 23×32×71

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 504 and 510 is 6

Greatest Common Factor of 504 and 510 by matching factors method

Factors of 504

List of positive integer factors of 504 that divides 504 without a remainder.

1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504

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 504 and 510. The biggest common factor number is the GCF number.
So the greatest common factor 504 and 510 is 6.

Also check out the Least Common Multiple of 504 and 510

Properties of GCF 504 and 510

(i) The GCF of 504 and 510 is associative

GCF of 504 and 510 = GCF of 510 and 504

Related Greatest Common Factor of 504

Related Greatest Common Factor of 510

Frequently Asked Questions on GCF of 504 and 510

1. What is the GCF of 504 and 510?

Answer: GCF of 504 and 510 is 6.

2. What are the Factors of 504?

Answer: Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. There are 24 integers that are factors of 504. The greatest factor of 504 is 504.

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 504 and 510?

Answer:

Greatest Common Factor of 504 and 510 = 6

Step 1: Find the prime factorization of 504

504 = 2 x 2 x 2 x 3 x 3 x 7

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 x 3 = 6

Step 4: Therefore, the greatest common factor of 504 and 510 is 6