What is the Greatest Common Factor of 19208 and 19222?

Greatest common factor (GCF) of 19208 and 19222 is 14.

GCF(19208,19222) = 14

We will now calculate the prime factors of 19208 and 19222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19208 and 19222.

How to find the GCF of 19208 and 19222?

We will first find the prime factorization of 19208 and 19222. After we will calculate the factors of 19208 and 19222 and find the biggest common factor number .

Step-1: Prime Factorization of 19208

Prime factors of 19208 are 2, 7. Prime factorization of 19208 in exponential form is:

19208 = 2³ × 7⁴

Step-2: Prime Factorization of 19222

Prime factors of 19222 are 2, 7, 1373. Prime factorization of 19222 in exponential form is:

19222 = 2¹ × 7¹ × 1373¹

Step-3: Factors of 19208

List of positive integer factors of 19208 that divides 19208 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2401, 2744, 4802, 9604

Step-4: Factors of 19222

List of positive integer factors of 19222 that divides 19208 without a remainder.

1, 2, 7, 14, 1373, 2746, 9611

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19208 and 19222. The biggest common factor number is the GCF number.
So the greatest common factor 19208 and 19222 is 14.

Also check out the Least Common Multiple of 19208 and 19222