What is the Greatest Common Factor of 59190 and 59200?

Greatest common factor (GCF) of 59190 and 59200 is 10.

GCF(59190,59200) = 10

We will now calculate the prime factors of 59190 and 59200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59190 and 59200.

How to find the GCF of 59190 and 59200?

We will first find the prime factorization of 59190 and 59200. After we will calculate the factors of 59190 and 59200 and find the biggest common factor number .

Step-1: Prime Factorization of 59190

Prime factors of 59190 are 2, 3, 5, 1973. Prime factorization of 59190 in exponential form is:

59190 = 2¹ × 3¹ × 5¹ × 1973¹

Step-2: 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-3: Factors of 59190

List of positive integer factors of 59190 that divides 59190 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1973, 3946, 5919, 9865, 11838, 19730, 29595

Step-4: Factors of 59200

List of positive integer factors of 59200 that divides 59190 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59190 and 59200. The biggest common factor number is the GCF number.
So the greatest common factor 59190 and 59200 is 10.

Also check out the Least Common Multiple of 59190 and 59200