Greatest Common Factor of 405 and 408

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 405, 408 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 405 and 408 is 3.

GCF(405,408) = 3

GCF of 405 and 408

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

GCF of:
and

Greatest Common Factor of 405 and 408

GCF of 405 and 408 is 3

Prime Factorization of 405


3 405
3 135
3 45
3 15
5 5
1

Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:

405 = 34×51

Prime Factorization of 408


2 408
2 204
2 102
3 51
17 17
1

Prime factors of 408 are 2,3,17. Prime factorization of 408 in exponential form is:

408 = 23×31×171

∴ So by taking common prime factors GCF of 405 and 408 is 3

Greatest Common Factor of 405 and 408 by matching factors method

Factors of 405

List of positive integer factors of 405 that divides 405 without a remainder.

1,3,5,9,15,27,45,81,135,405

Factors of 408

List of positive integer factors of 408 that divides 408 without a remainder.

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Greatest Common Factor

We found the factors and prime factorization of 405 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 405 and 408 is 3.

Also check out the Least Common Multiple of 405 and 408

Properties of GCF 405 and 408

(i) The GCF of 405 and 408 is associative

GCF of 405 and 408 = GCF of 408 and 405

Related Greatest Common Factor of 405

Related Greatest Common Factor of 408

Frequently Asked Questions on GCF of 405 and 408

1. What is the GCF of 405 and 408?

Answer: GCF of 405 and 408 is 3.

2. What are the Factors of 405?

Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.

3. What are the Factors of 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

4. How to Find the GCF of 405 and 408?

Answer:

Greatest Common Factor of 405 and 408 = 3

Step 1: Find the prime factorization of 405

405 = 3 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

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 405 and 408 is 3