What is the Greatest Common Factor of 19575 and 19590?

Greatest common factor (GCF) of 19575 and 19590 is 15.

GCF(19575,19590) = 15

We will now calculate the prime factors of 19575 and 19590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19575 and 19590.

How to find the GCF of 19575 and 19590?

We will first find the prime factorization of 19575 and 19590. After we will calculate the factors of 19575 and 19590 and find the biggest common factor number .

Step-1: Prime Factorization of 19575

Prime factors of 19575 are 3, 5, 29. Prime factorization of 19575 in exponential form is:

19575 = 3³ × 5² × 29¹

Step-2: 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-3: Factors of 19575

List of positive integer factors of 19575 that divides 19575 without a remainder.

1, 3, 5, 9, 15, 25, 27, 29, 45, 75, 87, 135, 145, 225, 261, 435, 675, 725, 783, 1305, 2175, 3915, 6525

Step-4: Factors of 19590

List of positive integer factors of 19590 that divides 19575 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19575 and 19590. The biggest common factor number is the GCF number.
So the greatest common factor 19575 and 19590 is 15.

Also check out the Least Common Multiple of 19575 and 19590