Greatest Common Factor of 408 and 409

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 408, 409 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 408 and 409 is 1.

GCF(408,409) = 1

GCF of 408 and 409

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

GCF of:
and

Greatest Common Factor of 408 and 409

GCF of 408 and 409 is 1

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

Prime Factorization of 409


409 409
1

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 4091

∴ So by taking common prime factors GCF of 408 and 409 is 1

Greatest Common Factor of 408 and 409 by matching factors method

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

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1,409

Greatest Common Factor

We found the factors and prime factorization of 408 and 409. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 409 is 1.

Also check out the Least Common Multiple of 408 and 409

Properties of GCF 408 and 409

(i) The GCF of 408 and 409 is associative

GCF of 408 and 409 = GCF of 409 and 408

Related Greatest Common Factor of 408

Related Greatest Common Factor of 409

Frequently Asked Questions on GCF of 408 and 409

1. What is the GCF of 408 and 409?

Answer: GCF of 408 and 409 is 1.

2. 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.

3. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

4. How to Find the GCF of 408 and 409?

Answer:

Greatest Common Factor of 408 and 409 = 1

Step 1: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

Step 2: Find the prime factorization of 409

409 = 409

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 408 and 409 is 1