Greatest Common Factor of 459 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 459, 465 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 459 and 465 is 3.

GCF(459,465) = 3

GCF of 459 and 465

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

GCF of:
and

Greatest Common Factor of 459 and 465

GCF of 459 and 465 is 3

Prime Factorization of 459


3 459
3 153
3 51
17 17
1

Prime factors of 459 are 3,17. Prime factorization of 459 in exponential form is:

459 = 33×171

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 459 and 465 is 3

Greatest Common Factor of 459 and 465 by matching factors method

Factors of 459

List of positive integer factors of 459 that divides 459 without a remainder.

1,3,9,17,27,51,153,459

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 459 and 465. The biggest common factor number is the GCF number.
So the greatest common factor 459 and 465 is 3.

Also check out the Least Common Multiple of 459 and 465

Properties of GCF 459 and 465

(i) The GCF of 459 and 465 is associative

GCF of 459 and 465 = GCF of 465 and 459

Related Greatest Common Factor of 459

Related Greatest Common Factor of 465

Frequently Asked Questions on GCF of 459 and 465

1. What is the GCF of 459 and 465?

Answer: GCF of 459 and 465 is 3.

2. What are the Factors of 459?

Answer: Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. There are 8 integers that are factors of 459. The greatest factor of 459 is 459.

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 459 and 465?

Answer:

Greatest Common Factor of 459 and 465 = 3

Step 1: Find the prime factorization of 459

459 = 3 x 3 x 3 x 17

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 = 3

Step 4: Therefore, the greatest common factor of 459 and 465 is 3