What is the Greatest Common Factor of 67208 and 67214?

Greatest common factor (GCF) of 67208 and 67214 is 2.

GCF(67208,67214) = 2

We will now calculate the prime factors of 67208 and 67214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67208 and 67214.

How to find the GCF of 67208 and 67214?

We will first find the prime factorization of 67208 and 67214. After we will calculate the factors of 67208 and 67214 and find the biggest common factor number .

Step-1: Prime Factorization of 67208

Prime factors of 67208 are 2, 31, 271. Prime factorization of 67208 in exponential form is:

67208 = 2³ × 31¹ × 271¹

Step-2: Prime Factorization of 67214

Prime factors of 67214 are 2, 7, 4801. Prime factorization of 67214 in exponential form is:

67214 = 2¹ × 7¹ × 4801¹

Step-3: Factors of 67208

List of positive integer factors of 67208 that divides 67208 without a remainder.

1, 2, 4, 8, 31, 62, 124, 248, 271, 542, 1084, 2168, 8401, 16802, 33604

Step-4: Factors of 67214

List of positive integer factors of 67214 that divides 67208 without a remainder.

1, 2, 7, 14, 4801, 9602, 33607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67208 and 67214. The biggest common factor number is the GCF number.
So the greatest common factor 67208 and 67214 is 2.

Also check out the Least Common Multiple of 67208 and 67214