Greatest Common Factor of 460 and 464

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 460, 464 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 460 and 464 is 4.

GCF(460,464) = 4

GCF of 460 and 464

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

GCF of:
and

Greatest Common Factor of 460 and 464

GCF of 460 and 464 is 4

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

Prime Factorization of 464


2 464
2 232
2 116
2 58
29 29
1

Prime factors of 464 are 2,29. Prime factorization of 464 in exponential form is:

464 = 24×291

∴ So by taking common prime factors GCF of 460 and 464 is 4

Greatest Common Factor of 460 and 464 by matching factors method

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

Factors of 464

List of positive integer factors of 464 that divides 464 without a remainder.

1,2,4,8,16,29,58,116,232,464

Greatest Common Factor

We found the factors and prime factorization of 460 and 464. The biggest common factor number is the GCF number.
So the greatest common factor 460 and 464 is 4.

Also check out the Least Common Multiple of 460 and 464

Properties of GCF 460 and 464

(i) The GCF of 460 and 464 is associative

GCF of 460 and 464 = GCF of 464 and 460

Related Greatest Common Factor of 460

Related Greatest Common Factor of 464

Frequently Asked Questions on GCF of 460 and 464

1. What is the GCF of 460 and 464?

Answer: GCF of 460 and 464 is 4.

2. 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.

3. What are the Factors of 464?

Answer: Factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. There are 10 integers that are factors of 464. The greatest factor of 464 is 464.

4. How to Find the GCF of 460 and 464?

Answer:

Greatest Common Factor of 460 and 464 = 4

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 464

464 = 2 x 2 x 2 x 2 x 29

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 460 and 464 is 4