What is the Greatest Common Factor of 51200 and 51216?

Greatest common factor (GCF) of 51200 and 51216 is 16.

GCF(51200,51216) = 16

We will now calculate the prime factors of 51200 and 51216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51200 and 51216.

How to find the GCF of 51200 and 51216?

We will first find the prime factorization of 51200 and 51216. After we will calculate the factors of 51200 and 51216 and find the biggest common factor number .

Step-1: Prime Factorization of 51200

Prime factors of 51200 are 2, 5. Prime factorization of 51200 in exponential form is:

51200 = 2¹¹ × 5²

Step-2: Prime Factorization of 51216

Prime factors of 51216 are 2, 3, 11, 97. Prime factorization of 51216 in exponential form is:

51216 = 2⁴ × 3¹ × 11¹ × 97¹

Step-3: Factors of 51200

List of positive integer factors of 51200 that divides 51200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2048, 2560, 3200, 5120, 6400, 10240, 12800, 25600

Step-4: Factors of 51216

List of positive integer factors of 51216 that divides 51200 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 97, 132, 176, 194, 264, 291, 388, 528, 582, 776, 1067, 1164, 1552, 2134, 2328, 3201, 4268, 4656, 6402, 8536, 12804, 17072, 25608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51200 and 51216. The biggest common factor number is the GCF number.
So the greatest common factor 51200 and 51216 is 16.

Also check out the Least Common Multiple of 51200 and 51216