What is the Greatest Common Factor of 19125 and 19140?

Greatest common factor (GCF) of 19125 and 19140 is 15.

GCF(19125,19140) = 15

We will now calculate the prime factors of 19125 and 19140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19125 and 19140.

How to find the GCF of 19125 and 19140?

We will first find the prime factorization of 19125 and 19140. After we will calculate the factors of 19125 and 19140 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19140

Prime factors of 19140 are 2, 3, 5, 11, 29. Prime factorization of 19140 in exponential form is:

19140 = 2² × 3¹ × 5¹ × 11¹ × 29¹

Step-3: Factors of 19125

List of positive integer factors of 19125 that divides 19125 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

Step-4: Factors of 19140

List of positive integer factors of 19140 that divides 19125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 29, 30, 33, 44, 55, 58, 60, 66, 87, 110, 116, 132, 145, 165, 174, 220, 290, 319, 330, 348, 435, 580, 638, 660, 870, 957, 1276, 1595, 1740, 1914, 3190, 3828, 4785, 6380, 9570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19125 and 19140. The biggest common factor number is the GCF number.
So the greatest common factor 19125 and 19140 is 15.

Also check out the Least Common Multiple of 19125 and 19140