What is the Greatest Common Factor of 59585 and 59600?

Greatest common factor (GCF) of 59585 and 59600 is 5.

GCF(59585,59600) = 5

We will now calculate the prime factors of 59585 and 59600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59585 and 59600.

How to find the GCF of 59585 and 59600?

We will first find the prime factorization of 59585 and 59600. After we will calculate the factors of 59585 and 59600 and find the biggest common factor number .

Step-1: Prime Factorization of 59585

Prime factors of 59585 are 5, 17, 701. Prime factorization of 59585 in exponential form is:

59585 = 5¹ × 17¹ × 701¹

Step-2: Prime Factorization of 59600

Prime factors of 59600 are 2, 5, 149. Prime factorization of 59600 in exponential form is:

59600 = 2⁴ × 5² × 149¹

Step-3: Factors of 59585

List of positive integer factors of 59585 that divides 59585 without a remainder.

1, 5, 17, 85, 701, 3505, 11917

Step-4: Factors of 59600

List of positive integer factors of 59600 that divides 59585 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 149, 200, 298, 400, 596, 745, 1192, 1490, 2384, 2980, 3725, 5960, 7450, 11920, 14900, 29800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59585 and 59600. The biggest common factor number is the GCF number.
So the greatest common factor 59585 and 59600 is 5.

Also check out the Least Common Multiple of 59585 and 59600