What is the Greatest Common Factor of 852 and 867?

Greatest common factor (GCF) of 852 and 867 is 3.

GCF(852,867) = 3

We will now calculate the prime factors of 852 and 867, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 852 and 867.

How to find the GCF of 852 and 867?

We will first find the prime factorization of 852 and 867. After we will calculate the factors of 852 and 867 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 867

Prime factors of 867 are 3, 17. Prime factorization of 867 in exponential form is:

867 = 3¹ × 17²

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 867

List of positive integer factors of 867 that divides 852 without a remainder.

1, 3, 17, 51, 289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 852 and 867. The biggest common factor number is the GCF number.
So the greatest common factor 852 and 867 is 3.

Also check out the Least Common Multiple of 852 and 867