What is the Greatest Common Factor of 67214 and 67228?

Greatest common factor (GCF) of 67214 and 67228 is 14.

GCF(67214,67228) = 14

We will now calculate the prime factors of 67214 and 67228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67214 and 67228.

How to find the GCF of 67214 and 67228?

We will first find the prime factorization of 67214 and 67228. After we will calculate the factors of 67214 and 67228 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67228

Prime factors of 67228 are 2, 7. Prime factorization of 67228 in exponential form is:

67228 = 2² × 7⁵

Step-3: Factors of 67214

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

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

Step-4: Factors of 67228

List of positive integer factors of 67228 that divides 67214 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604, 16807, 33614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67214 and 67228. The biggest common factor number is the GCF number.
So the greatest common factor 67214 and 67228 is 14.

Also check out the Least Common Multiple of 67214 and 67228