What is the Greatest Common Factor of 77200 and 77216?

Greatest common factor (GCF) of 77200 and 77216 is 16.

GCF(77200,77216) = 16

We will now calculate the prime factors of 77200 and 77216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77200 and 77216.

How to find the GCF of 77200 and 77216?

We will first find the prime factorization of 77200 and 77216. After we will calculate the factors of 77200 and 77216 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 77216

Prime factors of 77216 are 2, 19, 127. Prime factorization of 77216 in exponential form is:

77216 = 2⁵ × 19¹ × 127¹

Step-3: Factors of 77200

List of positive integer factors of 77200 that divides 77200 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

Step-4: Factors of 77216

List of positive integer factors of 77216 that divides 77200 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 76, 127, 152, 254, 304, 508, 608, 1016, 2032, 2413, 4064, 4826, 9652, 19304, 38608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77200 and 77216. The biggest common factor number is the GCF number.
So the greatest common factor 77200 and 77216 is 16.

Also check out the Least Common Multiple of 77200 and 77216