Greatest Common Factor of 410 and 416

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 410, 416 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 410 and 416 is 2.

GCF(410,416) = 2

GCF of 410 and 416

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

GCF of:
and

Greatest Common Factor of 410 and 416

GCF of 410 and 416 is 2

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

Prime Factorization of 416


2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:

416 = 25×131

∴ So by taking common prime factors GCF of 410 and 416 is 2

Greatest Common Factor of 410 and 416 by matching factors method

Factors of 410

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

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

Factors of 416

List of positive integer factors of 416 that divides 416 without a remainder.

1,2,4,8,13,16,26,32,52,104,208,416

Greatest Common Factor

We found the factors and prime factorization of 410 and 416. The biggest common factor number is the GCF number.
So the greatest common factor 410 and 416 is 2.

Also check out the Least Common Multiple of 410 and 416

Properties of GCF 410 and 416

(i) The GCF of 410 and 416 is associative

GCF of 410 and 416 = GCF of 416 and 410

Related Greatest Common Factor of 410

Related Greatest Common Factor of 416

Frequently Asked Questions on GCF of 410 and 416

1. What is the GCF of 410 and 416?

Answer: GCF of 410 and 416 is 2.

2. 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.

3. What are the Factors of 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

4. How to Find the GCF of 410 and 416?

Answer:

Greatest Common Factor of 410 and 416 = 2

Step 1: Find the prime factorization of 410

410 = 2 x 5 x 41

Step 2: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

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

GCF = 2

Step 4: Therefore, the greatest common factor of 410 and 416 is 2