Greatest Common Factor of 408 and 412

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, 412 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 408 and 412 is 4.

GCF(408,412) = 4

GCF of 408 and 412

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

GCF of:
and

Greatest Common Factor of 408 and 412

GCF of 408 and 412 is 4

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 412


2 412
2 206
103 103
1

Prime factors of 412 are 2,103. Prime factorization of 412 in exponential form is:

412 = 22×1031

∴ So by taking common prime factors GCF of 408 and 412 is 4

Greatest Common Factor of 408 and 412 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 412

List of positive integer factors of 412 that divides 412 without a remainder.

1,2,4,103,206,412

Greatest Common Factor

We found the factors and prime factorization of 408 and 412. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 412 is 4.

Also check out the Least Common Multiple of 408 and 412

Properties of GCF 408 and 412

(i) The GCF of 408 and 412 is associative

GCF of 408 and 412 = GCF of 412 and 408

Related Greatest Common Factor of 408

Related Greatest Common Factor of 412

Frequently Asked Questions on GCF of 408 and 412

1. What is the GCF of 408 and 412?

Answer: GCF of 408 and 412 is 4.

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 412?

Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.

4. How to Find the GCF of 408 and 412?

Answer:

Greatest Common Factor of 408 and 412 = 4

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 412

412 = 2 x 2 x 103

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 408 and 412 is 4