Greatest Common Factor of 408 and 414

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, 414 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 408 and 414 is 6.

GCF(408,414) = 6

GCF of 408 and 414

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

GCF of:
and

Greatest Common Factor of 408 and 414

GCF of 408 and 414 is 6

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 414


2 414
3 207
3 69
23 23
1

Prime factors of 414 are 2,3,23. Prime factorization of 414 in exponential form is:

414 = 21×32×231

∴ So by taking common prime factors GCF of 408 and 414 is 6

Greatest Common Factor of 408 and 414 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 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors and prime factorization of 408 and 414. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 414 is 6.

Also check out the Least Common Multiple of 408 and 414

Properties of GCF 408 and 414

(i) The GCF of 408 and 414 is associative

GCF of 408 and 414 = GCF of 414 and 408

Related Greatest Common Factor of 408

Related Greatest Common Factor of 414

Frequently Asked Questions on GCF of 408 and 414

1. What is the GCF of 408 and 414?

Answer: GCF of 408 and 414 is 6.

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 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

4. How to Find the GCF of 408 and 414?

Answer:

Greatest Common Factor of 408 and 414 = 6

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 414

414 = 2 x 3 x 3 x 23

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 408 and 414 is 6