What is the Greatest Common Factor of 59200 and 59213?

Greatest common factor (GCF) of 59200 and 59213 is 1.

GCF(59200,59213) = 1

We will now calculate the prime factors of 59200 and 59213, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59200 and 59213.

How to find the GCF of 59200 and 59213?

We will first find the prime factorization of 59200 and 59213. After we will calculate the factors of 59200 and 59213 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 59213

Prime factors of 59213 are 7, 11, 769. Prime factorization of 59213 in exponential form is:

59213 = 7¹ × 11¹ × 769¹

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 59213

List of positive integer factors of 59213 that divides 59200 without a remainder.

1, 7, 11, 77, 769, 5383, 8459

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59200 and 59213. The biggest common factor number is the GCF number.
So the greatest common factor 59200 and 59213 is 1.

Also check out the Least Common Multiple of 59200 and 59213