What is the Greatest Common Factor of 43198 and 43214?

Greatest common factor (GCF) of 43198 and 43214 is 2.

GCF(43198,43214) = 2

We will now calculate the prime factors of 43198 and 43214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43198 and 43214.

How to find the GCF of 43198 and 43214?

We will first find the prime factorization of 43198 and 43214. After we will calculate the factors of 43198 and 43214 and find the biggest common factor number .

Step-1: Prime Factorization of 43198

Prime factors of 43198 are 2, 21599. Prime factorization of 43198 in exponential form is:

43198 = 2¹ × 21599¹

Step-2: Prime Factorization of 43214

Prime factors of 43214 are 2, 17, 31, 41. Prime factorization of 43214 in exponential form is:

43214 = 2¹ × 17¹ × 31¹ × 41¹

Step-3: Factors of 43198

List of positive integer factors of 43198 that divides 43198 without a remainder.

1, 2, 21599

Step-4: Factors of 43214

List of positive integer factors of 43214 that divides 43198 without a remainder.

1, 2, 17, 31, 34, 41, 62, 82, 527, 697, 1054, 1271, 1394, 2542, 21607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43198 and 43214. The biggest common factor number is the GCF number.
So the greatest common factor 43198 and 43214 is 2.

Also check out the Least Common Multiple of 43198 and 43214