What is the Greatest Common Factor of 51200 and 51210?

Greatest common factor (GCF) of 51200 and 51210 is 10.

GCF(51200,51210) = 10

We will now calculate the prime factors of 51200 and 51210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51200 and 51210.

How to find the GCF of 51200 and 51210?

We will first find the prime factorization of 51200 and 51210. After we will calculate the factors of 51200 and 51210 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 51210

Prime factors of 51210 are 2, 3, 5, 569. Prime factorization of 51210 in exponential form is:

51210 = 2¹ × 3² × 5¹ × 569¹

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 51210

List of positive integer factors of 51210 that divides 51200 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 569, 1138, 1707, 2845, 3414, 5121, 5690, 8535, 10242, 17070, 25605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51200 and 51210. The biggest common factor number is the GCF number.
So the greatest common factor 51200 and 51210 is 10.

Also check out the Least Common Multiple of 51200 and 51210