What is the Greatest Common Factor of 59200 and 59210?

Greatest common factor (GCF) of 59200 and 59210 is 10.

GCF(59200,59210) = 10

We will now calculate the prime factors of 59200 and 59210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59200 and 59210.

How to find the GCF of 59200 and 59210?

We will first find the prime factorization of 59200 and 59210. After we will calculate the factors of 59200 and 59210 and find the biggest common factor number .

Step-1: Prime Factorization of 59200

Prime factors of 59200 are 2, 5, 37. Prime factorization of 59200 in exponential form is:

59200 = 2⁶ × 5² × 37¹

Step-2: Prime Factorization of 59210

Prime factors of 59210 are 2, 5, 31, 191. Prime factorization of 59210 in exponential form is:

59210 = 2¹ × 5¹ × 31¹ × 191¹

Step-3: Factors of 59200

List of positive integer factors of 59200 that divides 59200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 37, 40, 50, 64, 74, 80, 100, 148, 160, 185, 200, 296, 320, 370, 400, 592, 740, 800, 925, 1184, 1480, 1600, 1850, 2368, 2960, 3700, 5920, 7400, 11840, 14800, 29600

Step-4: Factors of 59210

List of positive integer factors of 59210 that divides 59200 without a remainder.

1, 2, 5, 10, 31, 62, 155, 191, 310, 382, 955, 1910, 5921, 11842, 29605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59200 and 59210. The biggest common factor number is the GCF number.
So the greatest common factor 59200 and 59210 is 10.

Also check out the Least Common Multiple of 59200 and 59210