What is the Greatest Common Factor of 19075 and 19082?

Greatest common factor (GCF) of 19075 and 19082 is 7.

GCF(19075,19082) = 7

We will now calculate the prime factors of 19075 and 19082, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19075 and 19082.

How to find the GCF of 19075 and 19082?

We will first find the prime factorization of 19075 and 19082. After we will calculate the factors of 19075 and 19082 and find the biggest common factor number .

Step-1: Prime Factorization of 19075

Prime factors of 19075 are 5, 7, 109. Prime factorization of 19075 in exponential form is:

19075 = 5² × 7¹ × 109¹

Step-2: Prime Factorization of 19082

Prime factors of 19082 are 2, 7, 29, 47. Prime factorization of 19082 in exponential form is:

19082 = 2¹ × 7¹ × 29¹ × 47¹

Step-3: Factors of 19075

List of positive integer factors of 19075 that divides 19075 without a remainder.

1, 5, 7, 25, 35, 109, 175, 545, 763, 2725, 3815

Step-4: Factors of 19082

List of positive integer factors of 19082 that divides 19075 without a remainder.

1, 2, 7, 14, 29, 47, 58, 94, 203, 329, 406, 658, 1363, 2726, 9541

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19075 and 19082. The biggest common factor number is the GCF number.
So the greatest common factor 19075 and 19082 is 7.

Also check out the Least Common Multiple of 19075 and 19082