Greatest Common Factor of 408 and 413

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

Greatest common factor (GCF) of 408 and 413 is 1.

GCF(408,413) = 1

GCF of 408 and 413

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

GCF of:
and

Greatest Common Factor of 408 and 413

GCF of 408 and 413 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 413


7 413
59 59
1

Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:

413 = 71×591

∴ So by taking common prime factors GCF of 408 and 413 is 1

Greatest Common Factor of 408 and 413 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 413

List of positive integer factors of 413 that divides 413 without a remainder.

1,7,59,413

Greatest Common Factor

We found the factors and prime factorization of 408 and 413. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 413 is 1.

Also check out the Least Common Multiple of 408 and 413

Properties of GCF 408 and 413

(i) The GCF of 408 and 413 is associative

GCF of 408 and 413 = GCF of 413 and 408

Related Greatest Common Factor of 408

Related Greatest Common Factor of 413

Frequently Asked Questions on GCF of 408 and 413

1. What is the GCF of 408 and 413?

Answer: GCF of 408 and 413 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 413?

Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.

4. How to Find the GCF of 408 and 413?

Answer:

Greatest Common Factor of 408 and 413 = 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 413

413 = 7 x 59

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 413 is 1