Greatest Common Factor of 456 and 460

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 456, 460 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 456 and 460 is 4.

GCF(456,460) = 4

GCF of 456 and 460

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

GCF of:
and

Greatest Common Factor of 456 and 460

GCF of 456 and 460 is 4

Prime Factorization of 456


2 456
2 228
2 114
3 57
19 19
1

Prime factors of 456 are 2,3,19. Prime factorization of 456 in exponential form is:

456 = 23×31×191

Prime Factorization of 460


2 460
2 230
5 115
23 23
1

Prime factors of 460 are 2,5,23. Prime factorization of 460 in exponential form is:

460 = 22×51×231

∴ So by taking common prime factors GCF of 456 and 460 is 4

Greatest Common Factor of 456 and 460 by matching factors method

Factors of 456

List of positive integer factors of 456 that divides 456 without a remainder.

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors and prime factorization of 456 and 460. The biggest common factor number is the GCF number.
So the greatest common factor 456 and 460 is 4.

Also check out the Least Common Multiple of 456 and 460

Properties of GCF 456 and 460

(i) The GCF of 456 and 460 is associative

GCF of 456 and 460 = GCF of 460 and 456

Related Greatest Common Factor of 456

Related Greatest Common Factor of 460

Frequently Asked Questions on GCF of 456 and 460

1. What is the GCF of 456 and 460?

Answer: GCF of 456 and 460 is 4.

2. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

3. What are the Factors of 460?

Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.

4. How to Find the GCF of 456 and 460?

Answer:

Greatest Common Factor of 456 and 460 = 4

Step 1: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

Step 2: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 456 and 460 is 4