Greatest Common Factor of 765 and 768

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 765, 768 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 765 and 768 is 3.

GCF(765,768) = 3

GCF of 765 and 768

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

GCF of:
and

Greatest Common Factor of 765 and 768

GCF of 765 and 768 is 3

Prime Factorization of 765


3 765
3 255
5 85
17 17
1

Prime factors of 765 are 3,5,17. Prime factorization of 765 in exponential form is:

765 = 32×51×171

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

∴ So by taking common prime factors GCF of 765 and 768 is 3

Greatest Common Factor of 765 and 768 by matching factors method

Factors of 765

List of positive integer factors of 765 that divides 765 without a remainder.

1,3,5,9,15,17,45,51,85,153,255,765

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

Greatest Common Factor

We found the factors and prime factorization of 765 and 768. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 768 is 3.

Also check out the Least Common Multiple of 765 and 768

Properties of GCF 765 and 768

(i) The GCF of 765 and 768 is associative

GCF of 765 and 768 = GCF of 768 and 765

Related Greatest Common Factor of 765

Related Greatest Common Factor of 768

Frequently Asked Questions on GCF of 765 and 768

1. What is the GCF of 765 and 768?

Answer: GCF of 765 and 768 is 3.

2. What are the Factors of 765?

Answer: Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765. There are 12 integers that are factors of 765. The greatest factor of 765 is 765.

3. 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.

4. How to Find the GCF of 765 and 768?

Answer:

Greatest Common Factor of 765 and 768 = 3

Step 1: Find the prime factorization of 765

765 = 3 x 3 x 5 x 17

Step 2: 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 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 765 and 768 is 3