Greatest Common Factor of 411 and 414

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 411, 414 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 411 and 414 is 3.

GCF(411,414) = 3

GCF of 411 and 414

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

GCF of:
and

Greatest Common Factor of 411 and 414

GCF of 411 and 414 is 3

Prime Factorization of 411


3 411
137 137
1

Prime factors of 411 are 3,137. Prime factorization of 411 in exponential form is:

411 = 31×1371

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

∴ So by taking common prime factors GCF of 411 and 414 is 3

Greatest Common Factor of 411 and 414 by matching factors method

Factors of 411

List of positive integer factors of 411 that divides 411 without a remainder.

1,3,137,411

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

Greatest Common Factor

We found the factors and prime factorization of 411 and 414. The biggest common factor number is the GCF number.
So the greatest common factor 411 and 414 is 3.

Also check out the Least Common Multiple of 411 and 414

Properties of GCF 411 and 414

(i) The GCF of 411 and 414 is associative

GCF of 411 and 414 = GCF of 414 and 411

Related Greatest Common Factor of 411

Related Greatest Common Factor of 414

Frequently Asked Questions on GCF of 411 and 414

1. What is the GCF of 411 and 414?

Answer: GCF of 411 and 414 is 3.

2. What are the Factors of 411?

Answer: Factors of 411 are 1, 3, 137, 411. There are 4 integers that are factors of 411. The greatest factor of 411 is 411.

3. 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.

4. How to Find the GCF of 411 and 414?

Answer:

Greatest Common Factor of 411 and 414 = 3

Step 1: Find the prime factorization of 411

411 = 3 x 137

Step 2: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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

GCF = 3

Step 4: Therefore, the greatest common factor of 411 and 414 is 3