Greatest Common Factor of 405 and 410

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 405, 410 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 405 and 410 is 5.

GCF(405,410) = 5

GCF of 405 and 410

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

GCF of:
and

Greatest Common Factor of 405 and 410

GCF of 405 and 410 is 5

Prime Factorization of 405


3 405
3 135
3 45
3 15
5 5
1

Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:

405 = 34×51

Prime Factorization of 410


2 410
5 205
41 41
1

Prime factors of 410 are 2,5,41. Prime factorization of 410 in exponential form is:

410 = 21×51×411

∴ So by taking common prime factors GCF of 405 and 410 is 5

Greatest Common Factor of 405 and 410 by matching factors method

Factors of 405

List of positive integer factors of 405 that divides 405 without a remainder.

1,3,5,9,15,27,45,81,135,405

Factors of 410

List of positive integer factors of 410 that divides 410 without a remainder.

1,2,5,10,41,82,205,410

Greatest Common Factor

We found the factors and prime factorization of 405 and 410. The biggest common factor number is the GCF number.
So the greatest common factor 405 and 410 is 5.

Also check out the Least Common Multiple of 405 and 410

Properties of GCF 405 and 410

(i) The GCF of 405 and 410 is associative

GCF of 405 and 410 = GCF of 410 and 405

Related Greatest Common Factor of 405

Related Greatest Common Factor of 410

Frequently Asked Questions on GCF of 405 and 410

1. What is the GCF of 405 and 410?

Answer: GCF of 405 and 410 is 5.

2. What are the Factors of 405?

Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.

3. What are the Factors of 410?

Answer: Factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410. There are 8 integers that are factors of 410. The greatest factor of 410 is 410.

4. How to Find the GCF of 405 and 410?

Answer:

Greatest Common Factor of 405 and 410 = 5

Step 1: Find the prime factorization of 405

405 = 3 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 410

410 = 2 x 5 x 41

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

GCF = 5

Step 4: Therefore, the greatest common factor of 405 and 410 is 5