Greatest Common Factor of 864 and 872

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 864, 872 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 864 and 872 is 8.

GCF(864,872) = 8

GCF of 864 and 872

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

GCF of:
and

Greatest Common Factor of 864 and 872

GCF of 864 and 872 is 8

Prime Factorization of 864


2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 864 are 2,3. Prime factorization of 864 in exponential form is:

864 = 25×33

Prime Factorization of 872


2 872
2 436
2 218
109 109
1

Prime factors of 872 are 2,109. Prime factorization of 872 in exponential form is:

872 = 23×1091

∴ So by taking common prime factors GCF of 864 and 872 is 8

Greatest Common Factor of 864 and 872 by matching factors method

Factors of 864

List of positive integer factors of 864 that divides 864 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864

Factors of 872

List of positive integer factors of 872 that divides 872 without a remainder.

1,2,4,8,109,218,436,872

Greatest Common Factor

We found the factors and prime factorization of 864 and 872. The biggest common factor number is the GCF number.
So the greatest common factor 864 and 872 is 8.

Also check out the Least Common Multiple of 864 and 872

Properties of GCF 864 and 872

(i) The GCF of 864 and 872 is associative

GCF of 864 and 872 = GCF of 872 and 864

Related Greatest Common Factor of 864

Related Greatest Common Factor of 872

Frequently Asked Questions on GCF of 864 and 872

1. What is the GCF of 864 and 872?

Answer: GCF of 864 and 872 is 8.

2. What are the Factors of 864?

Answer: Factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. There are 24 integers that are factors of 864. The greatest factor of 864 is 864.

3. What are the Factors of 872?

Answer: Factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872. There are 8 integers that are factors of 872. The greatest factor of 872 is 872.

4. How to Find the GCF of 864 and 872?

Answer:

Greatest Common Factor of 864 and 872 = 8

Step 1: Find the prime factorization of 864

864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 872

872 = 2 x 2 x 2 x 109

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 864 and 872 is 8