What is the Greatest Common Factor of 19116 and 19125?

Greatest common factor (GCF) of 19116 and 19125 is 9.

GCF(19116,19125) = 9

We will now calculate the prime factors of 19116 and 19125, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19116 and 19125.

How to find the GCF of 19116 and 19125?

We will first find the prime factorization of 19116 and 19125. After we will calculate the factors of 19116 and 19125 and find the biggest common factor number .

Step-1: Prime Factorization of 19116

Prime factors of 19116 are 2, 3, 59. Prime factorization of 19116 in exponential form is:

19116 = 2² × 3⁴ × 59¹

Step-2: Prime Factorization of 19125

Prime factors of 19125 are 3, 5, 17. Prime factorization of 19125 in exponential form is:

19125 = 3² × 5³ × 17¹

Step-3: Factors of 19116

List of positive integer factors of 19116 that divides 19116 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 59, 81, 108, 118, 162, 177, 236, 324, 354, 531, 708, 1062, 1593, 2124, 3186, 4779, 6372, 9558

Step-4: Factors of 19125

List of positive integer factors of 19125 that divides 19116 without a remainder.

1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 125, 153, 225, 255, 375, 425, 765, 1125, 1275, 2125, 3825, 6375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19116 and 19125. The biggest common factor number is the GCF number.
So the greatest common factor 19116 and 19125 is 9.

Also check out the Least Common Multiple of 19116 and 19125