Greatest Common Factor of 384 and 392

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 384, 392 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 384 and 392 is 8.

GCF(384,392) = 8

GCF of 384 and 392

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

GCF of:
and

Greatest Common Factor of 384 and 392

GCF of 384 and 392 is 8

Prime Factorization of 384


2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 384 are 2,3. Prime factorization of 384 in exponential form is:

384 = 27×31

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

∴ So by taking common prime factors GCF of 384 and 392 is 8

Greatest Common Factor of 384 and 392 by matching factors method

Factors of 384

List of positive integer factors of 384 that divides 384 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

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

Greatest Common Factor

We found the factors and prime factorization of 384 and 392. The biggest common factor number is the GCF number.
So the greatest common factor 384 and 392 is 8.

Also check out the Least Common Multiple of 384 and 392

Properties of GCF 384 and 392

(i) The GCF of 384 and 392 is associative

GCF of 384 and 392 = GCF of 392 and 384

Related Greatest Common Factor of 384

Related Greatest Common Factor of 392

Frequently Asked Questions on GCF of 384 and 392

1. What is the GCF of 384 and 392?

Answer: GCF of 384 and 392 is 8.

2. What are the Factors of 384?

Answer: Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. There are 16 integers that are factors of 384. The greatest factor of 384 is 384.

3. 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.

4. How to Find the GCF of 384 and 392?

Answer:

Greatest Common Factor of 384 and 392 = 8

Step 1: Find the prime factorization of 384

384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 392

392 = 2 x 2 x 2 x 7 x 7

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 384 and 392 is 8