What is the Greatest Common Factor of 77184 and 77200?

Greatest common factor (GCF) of 77184 and 77200 is 16.

GCF(77184,77200) = 16

We will now calculate the prime factors of 77184 and 77200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77184 and 77200.

How to find the GCF of 77184 and 77200?

We will first find the prime factorization of 77184 and 77200. After we will calculate the factors of 77184 and 77200 and find the biggest common factor number .

Step-1: Prime Factorization of 77184

Prime factors of 77184 are 2, 3, 67. Prime factorization of 77184 in exponential form is:

77184 = 2⁷ × 3² × 67¹

Step-2: Prime Factorization of 77200

Prime factors of 77200 are 2, 5, 193. Prime factorization of 77200 in exponential form is:

77200 = 2⁴ × 5² × 193¹

Step-3: Factors of 77184

List of positive integer factors of 77184 that divides 77184 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 67, 72, 96, 128, 134, 144, 192, 201, 268, 288, 384, 402, 536, 576, 603, 804, 1072, 1152, 1206, 1608, 2144, 2412, 3216, 4288, 4824, 6432, 8576, 9648, 12864, 19296, 25728, 38592

Step-4: Factors of 77200

List of positive integer factors of 77200 that divides 77184 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 193, 200, 386, 400, 772, 965, 1544, 1930, 3088, 3860, 4825, 7720, 9650, 15440, 19300, 38600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77184 and 77200. The biggest common factor number is the GCF number.
So the greatest common factor 77184 and 77200 is 16.

Also check out the Least Common Multiple of 77184 and 77200