Greatest Common Factor of 864 and 870

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

Greatest common factor (GCF) of 864 and 870 is 6.

GCF(864,870) = 6

GCF of 864 and 870

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

GCF of:
and

Greatest Common Factor of 864 and 870

GCF of 864 and 870 is 6

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 870


2 870
3 435
5 145
29 29
1

Prime factors of 870 are 2,3,5,29. Prime factorization of 870 in exponential form is:

870 = 21×31×51×291

∴ So by taking common prime factors GCF of 864 and 870 is 6

Greatest Common Factor of 864 and 870 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 870

List of positive integer factors of 870 that divides 870 without a remainder.

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors and prime factorization of 864 and 870. The biggest common factor number is the GCF number.
So the greatest common factor 864 and 870 is 6.

Also check out the Least Common Multiple of 864 and 870

Properties of GCF 864 and 870

(i) The GCF of 864 and 870 is associative

GCF of 864 and 870 = GCF of 870 and 864

Related Greatest Common Factor of 864

Related Greatest Common Factor of 870

Frequently Asked Questions on GCF of 864 and 870

1. What is the GCF of 864 and 870?

Answer: GCF of 864 and 870 is 6.

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 870?

Answer: Factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870. There are 16 integers that are factors of 870. The greatest factor of 870 is 870.

4. How to Find the GCF of 864 and 870?

Answer:

Greatest Common Factor of 864 and 870 = 6

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 870

870 = 2 x 3 x 5 x 29

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 864 and 870 is 6