What is the Greatest Common Factor of 864 and 870?

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

GCF(864,870) = 6

We will now calculate the prime factors of 864 and 870, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 864 and 870.

How to find the GCF of 864 and 870?

We will first find the prime factorization of 864 and 870. After we will calculate the factors of 864 and 870 and find the biggest common factor number .

Step-1: Prime Factorization of 864

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

864 = 2⁵ × 3³

Step-2: Prime Factorization of 870

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

870 = 2¹ × 3¹ × 5¹ × 29¹

Step-3: 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

Step-4: Factors of 870

List of positive integer factors of 870 that divides 864 without a remainder.

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

Final Step: Biggest Common Factor Number

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