Greatest Common Factor of 406 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 406, 413 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 406 and 413 is 7.

GCF(406,413) = 7

GCF of 406 and 413

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

GCF of:
and

Greatest Common Factor of 406 and 413

GCF of 406 and 413 is 7

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 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 406 and 413 is 7

Greatest Common Factor of 406 and 413 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 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 406 and 413. The biggest common factor number is the GCF number.
So the greatest common factor 406 and 413 is 7.

Also check out the Least Common Multiple of 406 and 413

Properties of GCF 406 and 413

(i) The GCF of 406 and 413 is associative

GCF of 406 and 413 = GCF of 413 and 406

Related Greatest Common Factor of 406

Related Greatest Common Factor of 413

Frequently Asked Questions on GCF of 406 and 413

1. What is the GCF of 406 and 413?

Answer: GCF of 406 and 413 is 7.

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 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 406 and 413?

Answer:

Greatest Common Factor of 406 and 413 = 7

Step 1: Find the prime factorization of 406

406 = 2 x 7 x 29

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 = 7

Step 4: Therefore, the greatest common factor of 406 and 413 is 7