What is the Greatest Common Factor of 43208 and 43214?

Greatest common factor (GCF) of 43208 and 43214 is 2.

GCF(43208,43214) = 2

We will now calculate the prime factors of 43208 and 43214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43208 and 43214.

How to find the GCF of 43208 and 43214?

We will first find the prime factorization of 43208 and 43214. After we will calculate the factors of 43208 and 43214 and find the biggest common factor number .

Step-1: Prime Factorization of 43208

Prime factors of 43208 are 2, 11, 491. Prime factorization of 43208 in exponential form is:

43208 = 2³ × 11¹ × 491¹

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 43208

List of positive integer factors of 43208 that divides 43208 without a remainder.

1, 2, 4, 8, 11, 22, 44, 88, 491, 982, 1964, 3928, 5401, 10802, 21604

Step-4: Factors of 43214

List of positive integer factors of 43214 that divides 43208 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 43208 and 43214. The biggest common factor number is the GCF number.
So the greatest common factor 43208 and 43214 is 2.

Also check out the Least Common Multiple of 43208 and 43214