Greatest Common Factor of 768 and 774

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 768, 774 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 768 and 774 is 6.

GCF(768,774) = 6

GCF of 768 and 774

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

GCF of:
and

Greatest Common Factor of 768 and 774

GCF of 768 and 774 is 6

Prime Factorization of 768


2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 768 are 2,3. Prime factorization of 768 in exponential form is:

768 = 28×31

Prime Factorization of 774


2 774
3 387
3 129
43 43
1

Prime factors of 774 are 2,3,43. Prime factorization of 774 in exponential form is:

774 = 21×32×431

∴ So by taking common prime factors GCF of 768 and 774 is 6

Greatest Common Factor of 768 and 774 by matching factors method

Factors of 768

List of positive integer factors of 768 that divides 768 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Factors of 774

List of positive integer factors of 774 that divides 774 without a remainder.

1,2,3,6,9,18,43,86,129,258,387,774

Greatest Common Factor

We found the factors and prime factorization of 768 and 774. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 774 is 6.

Also check out the Least Common Multiple of 768 and 774

Properties of GCF 768 and 774

(i) The GCF of 768 and 774 is associative

GCF of 768 and 774 = GCF of 774 and 768

Related Greatest Common Factor of 768

Related Greatest Common Factor of 774

Frequently Asked Questions on GCF of 768 and 774

1. What is the GCF of 768 and 774?

Answer: GCF of 768 and 774 is 6.

2. What are the Factors of 768?

Answer: Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. There are 18 integers that are factors of 768. The greatest factor of 768 is 768.

3. What are the Factors of 774?

Answer: Factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774. There are 12 integers that are factors of 774. The greatest factor of 774 is 774.

4. How to Find the GCF of 768 and 774?

Answer:

Greatest Common Factor of 768 and 774 = 6

Step 1: Find the prime factorization of 768

768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 774

774 = 2 x 3 x 3 x 43

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 768 and 774 is 6