What is the Greatest Common Factor of 51200 and 51205?

Greatest common factor (GCF) of 51200 and 51205 is 5.

GCF(51200,51205) = 5

We will now calculate the prime factors of 51200 and 51205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51200 and 51205.

How to find the GCF of 51200 and 51205?

We will first find the prime factorization of 51200 and 51205. After we will calculate the factors of 51200 and 51205 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 51205

Prime factors of 51205 are 5, 7, 11, 19. Prime factorization of 51205 in exponential form is:

51205 = 5¹ × 7² × 11¹ × 19¹

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 51205

List of positive integer factors of 51205 that divides 51200 without a remainder.

1, 5, 7, 11, 19, 35, 49, 55, 77, 95, 133, 209, 245, 385, 539, 665, 931, 1045, 1463, 2695, 4655, 7315, 10241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51200 and 51205. The biggest common factor number is the GCF number.
So the greatest common factor 51200 and 51205 is 5.

Also check out the Least Common Multiple of 51200 and 51205