What is the Greatest Common Factor of 19175 and 19188?

Greatest common factor (GCF) of 19175 and 19188 is 13.

GCF(19175,19188) = 13

We will now calculate the prime factors of 19175 and 19188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19175 and 19188.

How to find the GCF of 19175 and 19188?

We will first find the prime factorization of 19175 and 19188. After we will calculate the factors of 19175 and 19188 and find the biggest common factor number .

Step-1: Prime Factorization of 19175

Prime factors of 19175 are 5, 13, 59. Prime factorization of 19175 in exponential form is:

19175 = 5² × 13¹ × 59¹

Step-2: Prime Factorization of 19188

Prime factors of 19188 are 2, 3, 13, 41. Prime factorization of 19188 in exponential form is:

19188 = 2² × 3² × 13¹ × 41¹

Step-3: Factors of 19175

List of positive integer factors of 19175 that divides 19175 without a remainder.

1, 5, 13, 25, 59, 65, 295, 325, 767, 1475, 3835

Step-4: Factors of 19188

List of positive integer factors of 19188 that divides 19175 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 41, 52, 78, 82, 117, 123, 156, 164, 234, 246, 369, 468, 492, 533, 738, 1066, 1476, 1599, 2132, 3198, 4797, 6396, 9594

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19175 and 19188. The biggest common factor number is the GCF number.
So the greatest common factor 19175 and 19188 is 13.

Also check out the Least Common Multiple of 19175 and 19188