Greatest Common Factor of 378 and 384

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 378, 384 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 378 and 384 is 6.

GCF(378,384) = 6

GCF of 378 and 384

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

GCF of:
and

Greatest Common Factor of 378 and 384

GCF of 378 and 384 is 6

Prime Factorization of 378


2 378
3 189
3 63
3 21
7 7
1

Prime factors of 378 are 2,3,7. Prime factorization of 378 in exponential form is:

378 = 21×33×71

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

∴ So by taking common prime factors GCF of 378 and 384 is 6

Greatest Common Factor of 378 and 384 by matching factors method

Factors of 378

List of positive integer factors of 378 that divides 378 without a remainder.

1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378

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

Greatest Common Factor

We found the factors and prime factorization of 378 and 384. The biggest common factor number is the GCF number.
So the greatest common factor 378 and 384 is 6.

Also check out the Least Common Multiple of 378 and 384

Properties of GCF 378 and 384

(i) The GCF of 378 and 384 is associative

GCF of 378 and 384 = GCF of 384 and 378

Related Greatest Common Factor of 378

Related Greatest Common Factor of 384

Frequently Asked Questions on GCF of 378 and 384

1. What is the GCF of 378 and 384?

Answer: GCF of 378 and 384 is 6.

2. What are the Factors of 378?

Answer: Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. There are 16 integers that are factors of 378. The greatest factor of 378 is 378.

3. 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.

4. How to Find the GCF of 378 and 384?

Answer:

Greatest Common Factor of 378 and 384 = 6

Step 1: Find the prime factorization of 378

378 = 2 x 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 384

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

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 378 and 384 is 6