What is the Greatest Common Factor of 19125 and 19142?

Greatest common factor (GCF) of 19125 and 19142 is 17.

GCF(19125,19142) = 17

We will now calculate the prime factors of 19125 and 19142, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19125 and 19142.

How to find the GCF of 19125 and 19142?

We will first find the prime factorization of 19125 and 19142. After we will calculate the factors of 19125 and 19142 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 19142

Prime factors of 19142 are 2, 17, 563. Prime factorization of 19142 in exponential form is:

19142 = 2¹ × 17¹ × 563¹

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 19142

List of positive integer factors of 19142 that divides 19125 without a remainder.

1, 2, 17, 34, 563, 1126, 9571

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19125 and 19142. The biggest common factor number is the GCF number.
So the greatest common factor 19125 and 19142 is 17.

Also check out the Least Common Multiple of 19125 and 19142