What is the Greatest Common Factor of 76188 and 76200?

Greatest common factor (GCF) of 76188 and 76200 is 12.

GCF(76188,76200) = 12

We will now calculate the prime factors of 76188 and 76200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76188 and 76200.

How to find the GCF of 76188 and 76200?

We will first find the prime factorization of 76188 and 76200. After we will calculate the factors of 76188 and 76200 and find the biggest common factor number .

Step-1: Prime Factorization of 76188

Prime factors of 76188 are 2, 3, 7, 907. Prime factorization of 76188 in exponential form is:

76188 = 2² × 3¹ × 7¹ × 907¹

Step-2: Prime Factorization of 76200

Prime factors of 76200 are 2, 3, 5, 127. Prime factorization of 76200 in exponential form is:

76200 = 2³ × 3¹ × 5² × 127¹

Step-3: Factors of 76188

List of positive integer factors of 76188 that divides 76188 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 907, 1814, 2721, 3628, 5442, 6349, 10884, 12698, 19047, 25396, 38094

Step-4: Factors of 76200

List of positive integer factors of 76200 that divides 76188 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 127, 150, 200, 254, 300, 381, 508, 600, 635, 762, 1016, 1270, 1524, 1905, 2540, 3048, 3175, 3810, 5080, 6350, 7620, 9525, 12700, 15240, 19050, 25400, 38100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76188 and 76200. The biggest common factor number is the GCF number.
So the greatest common factor 76188 and 76200 is 12.

Also check out the Least Common Multiple of 76188 and 76200