Greatest Common Factor of 406 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 406, 408 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 406 and 408 is 2.

GCF(406,408) = 2

GCF of 406 and 408

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

GCF of:
and

Greatest Common Factor of 406 and 408

GCF of 406 and 408 is 2

Prime Factorization of 406


2 406
7 203
29 29
1

Prime factors of 406 are 2,7,29. Prime factorization of 406 in exponential form is:

406 = 21×71×291

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 406 and 408 is 2

Greatest Common Factor of 406 and 408 by matching factors method

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1,2,7,14,29,58,203,406

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 406 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 406 and 408 is 2.

Also check out the Least Common Multiple of 406 and 408

Properties of GCF 406 and 408

(i) The GCF of 406 and 408 is associative

GCF of 406 and 408 = GCF of 408 and 406

Related Greatest Common Factor of 406

Related Greatest Common Factor of 408

Frequently Asked Questions on GCF of 406 and 408

1. What is the GCF of 406 and 408?

Answer: GCF of 406 and 408 is 2.

2. What are the Factors of 406?

Answer: Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406. There are 8 integers that are factors of 406. The greatest factor of 406 is 406.

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 406 and 408?

Answer:

Greatest Common Factor of 406 and 408 = 2

Step 1: Find the prime factorization of 406

406 = 2 x 7 x 29

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 = 2

Step 4: Therefore, the greatest common factor of 406 and 408 is 2