Greatest Common Factor of 458 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 458, 460 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 458 and 460 is 2.

GCF(458,460) = 2

GCF of 458 and 460

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

GCF of:
and

Greatest Common Factor of 458 and 460

GCF of 458 and 460 is 2

Prime Factorization of 458


2 458
229 229
1

Prime factors of 458 are 2,229. Prime factorization of 458 in exponential form is:

458 = 21×2291

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 458 and 460 is 2

Greatest Common Factor of 458 and 460 by matching factors method

Factors of 458

List of positive integer factors of 458 that divides 458 without a remainder.

1,2,229,458

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 458 and 460. The biggest common factor number is the GCF number.
So the greatest common factor 458 and 460 is 2.

Also check out the Least Common Multiple of 458 and 460

Properties of GCF 458 and 460

(i) The GCF of 458 and 460 is associative

GCF of 458 and 460 = GCF of 460 and 458

Related Greatest Common Factor of 458

Related Greatest Common Factor of 460

Frequently Asked Questions on GCF of 458 and 460

1. What is the GCF of 458 and 460?

Answer: GCF of 458 and 460 is 2.

2. What are the Factors of 458?

Answer: Factors of 458 are 1, 2, 229, 458. There are 4 integers that are factors of 458. The greatest factor of 458 is 458.

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 458 and 460?

Answer:

Greatest Common Factor of 458 and 460 = 2

Step 1: Find the prime factorization of 458

458 = 2 x 229

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

Step 4: Therefore, the greatest common factor of 458 and 460 is 2