What is the Greatest Common Factor of 19201 and 19214?

Greatest common factor (GCF) of 19201 and 19214 is 13.

GCF(19201,19214) = 13

We will now calculate the prime factors of 19201 and 19214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19201 and 19214.

How to find the GCF of 19201 and 19214?

We will first find the prime factorization of 19201 and 19214. After we will calculate the factors of 19201 and 19214 and find the biggest common factor number .

Step-1: Prime Factorization of 19201

Prime factors of 19201 are 7, 13, 211. Prime factorization of 19201 in exponential form is:

19201 = 7¹ × 13¹ × 211¹

Step-2: Prime Factorization of 19214

Prime factors of 19214 are 2, 13, 739. Prime factorization of 19214 in exponential form is:

19214 = 2¹ × 13¹ × 739¹

Step-3: Factors of 19201

List of positive integer factors of 19201 that divides 19201 without a remainder.

1, 7, 13, 91, 211, 1477, 2743

Step-4: Factors of 19214

List of positive integer factors of 19214 that divides 19201 without a remainder.

1, 2, 13, 26, 739, 1478, 9607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19201 and 19214. The biggest common factor number is the GCF number.
So the greatest common factor 19201 and 19214 is 13.

Also check out the Least Common Multiple of 19201 and 19214