Greatest Common Factor of 414 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 414, 416 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 414 and 416 is 2.

GCF(414,416) = 2

GCF of 414 and 416

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

GCF of:
and

Greatest Common Factor of 414 and 416

GCF of 414 and 416 is 2

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

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 414 and 416 is 2

Greatest Common Factor of 414 and 416 by matching factors method

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

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 414 and 416. The biggest common factor number is the GCF number.
So the greatest common factor 414 and 416 is 2.

Also check out the Least Common Multiple of 414 and 416

Properties of GCF 414 and 416

(i) The GCF of 414 and 416 is associative

GCF of 414 and 416 = GCF of 416 and 414

Related Greatest Common Factor of 414

Related Greatest Common Factor of 416

Frequently Asked Questions on GCF of 414 and 416

1. What is the GCF of 414 and 416?

Answer: GCF of 414 and 416 is 2.

2. 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.

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 414 and 416?

Answer:

Greatest Common Factor of 414 and 416 = 2

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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 414 and 416 is 2