What is the Greatest Common Factor of 864 and 882?

Greatest common factor (GCF) of 864 and 882 is 18.

GCF(864,882) = 18

We will now calculate the prime factors of 864 and 882, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 864 and 882.

How to find the GCF of 864 and 882?

We will first find the prime factorization of 864 and 882. After we will calculate the factors of 864 and 882 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 882

Prime factors of 882 are 2, 3, 7. Prime factorization of 882 in exponential form is:

882 = 2¹ × 3² × 7²

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 882

List of positive integer factors of 882 that divides 864 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 864 and 882. The biggest common factor number is the GCF number.
So the greatest common factor 864 and 882 is 18.

Also check out the Least Common Multiple of 864 and 882