Greatest Common Factor of 768 and 772

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, 772 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 768 and 772 is 4.

GCF(768,772) = 4

GCF of 768 and 772

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

GCF of:
and

Greatest Common Factor of 768 and 772

GCF of 768 and 772 is 4

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 772


2 772
2 386
193 193
1

Prime factors of 772 are 2,193. Prime factorization of 772 in exponential form is:

772 = 22×1931

∴ So by taking common prime factors GCF of 768 and 772 is 4

Greatest Common Factor of 768 and 772 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 772

List of positive integer factors of 772 that divides 772 without a remainder.

1,2,4,193,386,772

Greatest Common Factor

We found the factors and prime factorization of 768 and 772. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 772 is 4.

Also check out the Least Common Multiple of 768 and 772

Properties of GCF 768 and 772

(i) The GCF of 768 and 772 is associative

GCF of 768 and 772 = GCF of 772 and 768

Related Greatest Common Factor of 768

Related Greatest Common Factor of 772

Frequently Asked Questions on GCF of 768 and 772

1. What is the GCF of 768 and 772?

Answer: GCF of 768 and 772 is 4.

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 772?

Answer: Factors of 772 are 1, 2, 4, 193, 386, 772. There are 6 integers that are factors of 772. The greatest factor of 772 is 772.

4. How to Find the GCF of 768 and 772?

Answer:

Greatest Common Factor of 768 and 772 = 4

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 772

772 = 2 x 2 x 193

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 768 and 772 is 4