What is the Greatest Common Factor of 852 and 864?

Greatest common factor (GCF) of 852 and 864 is 12.

GCF(852,864) = 12

We will now calculate the prime factors of 852 and 864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 852 and 864.

How to find the GCF of 852 and 864?

We will first find the prime factorization of 852 and 864. After we will calculate the factors of 852 and 864 and find the biggest common factor number .

Step-1: Prime Factorization of 852

Prime factors of 852 are 2, 3, 71. Prime factorization of 852 in exponential form is:

852 = 2² × 3¹ × 71¹

Step-2: Prime Factorization of 864

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

864 = 2⁵ × 3³

Step-3: Factors of 852

List of positive integer factors of 852 that divides 852 without a remainder.

1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426

Step-4: Factors of 864

List of positive integer factors of 864 that divides 852 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 852 and 864. The biggest common factor number is the GCF number.
So the greatest common factor 852 and 864 is 12.

Also check out the Least Common Multiple of 852 and 864