What is the Greatest Common Factor of 85872 and 85884?

Greatest common factor (GCF) of 85872 and 85884 is 12.

GCF(85872,85884) = 12

We will now calculate the prime factors of 85872 and 85884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85872 and 85884.

How to find the GCF of 85872 and 85884?

We will first find the prime factorization of 85872 and 85884. After we will calculate the factors of 85872 and 85884 and find the biggest common factor number .

Step-1: Prime Factorization of 85872

Prime factors of 85872 are 2, 3, 1789. Prime factorization of 85872 in exponential form is:

85872 = 2⁴ × 3¹ × 1789¹

Step-2: Prime Factorization of 85884

Prime factors of 85884 are 2, 3, 17, 421. Prime factorization of 85884 in exponential form is:

85884 = 2² × 3¹ × 17¹ × 421¹

Step-3: Factors of 85872

List of positive integer factors of 85872 that divides 85872 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1789, 3578, 5367, 7156, 10734, 14312, 21468, 28624, 42936

Step-4: Factors of 85884

List of positive integer factors of 85884 that divides 85872 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 421, 842, 1263, 1684, 2526, 5052, 7157, 14314, 21471, 28628, 42942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85872 and 85884. The biggest common factor number is the GCF number.
So the greatest common factor 85872 and 85884 is 12.

Also check out the Least Common Multiple of 85872 and 85884