Greatest Common Factor of 392 and 400

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 392, 400 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 392 and 400 is 8.

GCF(392,400) = 8

GCF of 392 and 400

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

GCF of:
and

Greatest Common Factor of 392 and 400

GCF of 392 and 400 is 8

Prime Factorization of 392


2 392
2 196
2 98
7 49
7 7
1

Prime factors of 392 are 2,7. Prime factorization of 392 in exponential form is:

392 = 23×72

Prime Factorization of 400


2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 400 are 2,5. Prime factorization of 400 in exponential form is:

400 = 24×52

∴ So by taking common prime factors GCF of 392 and 400 is 8

Greatest Common Factor of 392 and 400 by matching factors method

Factors of 392

List of positive integer factors of 392 that divides 392 without a remainder.

1,2,4,7,8,14,28,49,56,98,196,392

Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Greatest Common Factor

We found the factors and prime factorization of 392 and 400. The biggest common factor number is the GCF number.
So the greatest common factor 392 and 400 is 8.

Also check out the Least Common Multiple of 392 and 400

Properties of GCF 392 and 400

(i) The GCF of 392 and 400 is associative

GCF of 392 and 400 = GCF of 400 and 392

Related Greatest Common Factor of 392

Related Greatest Common Factor of 400

Frequently Asked Questions on GCF of 392 and 400

1. What is the GCF of 392 and 400?

Answer: GCF of 392 and 400 is 8.

2. What are the Factors of 392?

Answer: Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. There are 12 integers that are factors of 392. The greatest factor of 392 is 392.

3. What are the Factors of 400?

Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.

4. How to Find the GCF of 392 and 400?

Answer:

Greatest Common Factor of 392 and 400 = 8

Step 1: Find the prime factorization of 392

392 = 2 x 2 x 2 x 7 x 7

Step 2: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 x 5

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 392 and 400 is 8