What is the Greatest Common Factor of 19585 and 19600?

Greatest common factor (GCF) of 19585 and 19600 is 5.

GCF(19585,19600) = 5

We will now calculate the prime factors of 19585 and 19600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19585 and 19600.

How to find the GCF of 19585 and 19600?

We will first find the prime factorization of 19585 and 19600. After we will calculate the factors of 19585 and 19600 and find the biggest common factor number .

Step-1: Prime Factorization of 19585

Prime factors of 19585 are 5, 3917. Prime factorization of 19585 in exponential form is:

19585 = 5¹ × 3917¹

Step-2: Prime Factorization of 19600

Prime factors of 19600 are 2, 5, 7. Prime factorization of 19600 in exponential form is:

19600 = 2⁴ × 5² × 7²

Step-3: Factors of 19585

List of positive integer factors of 19585 that divides 19585 without a remainder.

1, 5, 3917

Step-4: Factors of 19600

List of positive integer factors of 19600 that divides 19585 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 49, 50, 56, 70, 80, 98, 100, 112, 140, 175, 196, 200, 245, 280, 350, 392, 400, 490, 560, 700, 784, 980, 1225, 1400, 1960, 2450, 2800, 3920, 4900, 9800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19585 and 19600. The biggest common factor number is the GCF number.
So the greatest common factor 19585 and 19600 is 5.

Also check out the Least Common Multiple of 19585 and 19600