What is the Greatest Common Factor of 84900 and 84912?

Greatest common factor (GCF) of 84900 and 84912 is 12.

GCF(84900,84912) = 12

We will now calculate the prime factors of 84900 and 84912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84900 and 84912.

How to find the GCF of 84900 and 84912?

We will first find the prime factorization of 84900 and 84912. After we will calculate the factors of 84900 and 84912 and find the biggest common factor number .

Step-1: Prime Factorization of 84900

Prime factors of 84900 are 2, 3, 5, 283. Prime factorization of 84900 in exponential form is:

84900 = 2² × 3¹ × 5² × 283¹

Step-2: Prime Factorization of 84912

Prime factors of 84912 are 2, 3, 29, 61. Prime factorization of 84912 in exponential form is:

84912 = 2⁴ × 3¹ × 29¹ × 61¹

Step-3: Factors of 84900

List of positive integer factors of 84900 that divides 84900 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 283, 300, 566, 849, 1132, 1415, 1698, 2830, 3396, 4245, 5660, 7075, 8490, 14150, 16980, 21225, 28300, 42450

Step-4: Factors of 84912

List of positive integer factors of 84912 that divides 84900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 58, 61, 87, 116, 122, 174, 183, 232, 244, 348, 366, 464, 488, 696, 732, 976, 1392, 1464, 1769, 2928, 3538, 5307, 7076, 10614, 14152, 21228, 28304, 42456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84900 and 84912. The biggest common factor number is the GCF number.
So the greatest common factor 84900 and 84912 is 12.

Also check out the Least Common Multiple of 84900 and 84912