What is the Greatest Common Factor of 43204 and 43214?

Greatest common factor (GCF) of 43204 and 43214 is 2.

GCF(43204,43214) = 2

We will now calculate the prime factors of 43204 and 43214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43204 and 43214.

How to find the GCF of 43204 and 43214?

We will first find the prime factorization of 43204 and 43214. After we will calculate the factors of 43204 and 43214 and find the biggest common factor number .

Step-1: Prime Factorization of 43204

Prime factors of 43204 are 2, 7, 1543. Prime factorization of 43204 in exponential form is:

43204 = 2² × 7¹ × 1543¹

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 43204

List of positive integer factors of 43204 that divides 43204 without a remainder.

1, 2, 4, 7, 14, 28, 1543, 3086, 6172, 10801, 21602

Step-4: Factors of 43214

List of positive integer factors of 43214 that divides 43204 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 43204 and 43214. The biggest common factor number is the GCF number.
So the greatest common factor 43204 and 43214 is 2.

Also check out the Least Common Multiple of 43204 and 43214