Greatest Common Factor of 460 and 465

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, 465 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 460 and 465 is 5.

GCF(460,465) = 5

GCF of 460 and 465

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

GCF of:
and

Greatest Common Factor of 460 and 465

GCF of 460 and 465 is 5

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 465


3 465
5 155
31 31
1

Prime factors of 465 are 3,5,31. Prime factorization of 465 in exponential form is:

465 = 31×51×311

∴ So by taking common prime factors GCF of 460 and 465 is 5

Greatest Common Factor of 460 and 465 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 465

List of positive integer factors of 465 that divides 465 without a remainder.

1,3,5,15,31,93,155,465

Greatest Common Factor

We found the factors and prime factorization of 460 and 465. The biggest common factor number is the GCF number.
So the greatest common factor 460 and 465 is 5.

Also check out the Least Common Multiple of 460 and 465

Properties of GCF 460 and 465

(i) The GCF of 460 and 465 is associative

GCF of 460 and 465 = GCF of 465 and 460

Related Greatest Common Factor of 460

Related Greatest Common Factor of 465

Frequently Asked Questions on GCF of 460 and 465

1. What is the GCF of 460 and 465?

Answer: GCF of 460 and 465 is 5.

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 465?

Answer: Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. There are 8 integers that are factors of 465. The greatest factor of 465 is 465.

4. How to Find the GCF of 460 and 465?

Answer:

Greatest Common Factor of 460 and 465 = 5

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 465

465 = 3 x 5 x 31

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

GCF = 5

Step 4: Therefore, the greatest common factor of 460 and 465 is 5