What is the Greatest Common Factor of 19590 and 19600?

Greatest common factor (GCF) of 19590 and 19600 is 10.

GCF(19590,19600) = 10

We will now calculate the prime factors of 19590 and 19600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19590 and 19600.

How to find the GCF of 19590 and 19600?

We will first find the prime factorization of 19590 and 19600. After we will calculate the factors of 19590 and 19600 and find the biggest common factor number .

Step-1: Prime Factorization of 19590

Prime factors of 19590 are 2, 3, 5, 653. Prime factorization of 19590 in exponential form is:

19590 = 2¹ × 3¹ × 5¹ × 653¹

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 19590

List of positive integer factors of 19590 that divides 19590 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 653, 1306, 1959, 3265, 3918, 6530, 9795

Step-4: Factors of 19600

List of positive integer factors of 19600 that divides 19590 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 19590 and 19600. The biggest common factor number is the GCF number.
So the greatest common factor 19590 and 19600 is 10.

Also check out the Least Common Multiple of 19590 and 19600