What is the Greatest Common Factor of 27208 and 27214?

Greatest common factor (GCF) of 27208 and 27214 is 2.

GCF(27208,27214) = 2

We will now calculate the prime factors of 27208 and 27214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27208 and 27214.

How to find the GCF of 27208 and 27214?

We will first find the prime factorization of 27208 and 27214. After we will calculate the factors of 27208 and 27214 and find the biggest common factor number .

Step-1: Prime Factorization of 27208

Prime factors of 27208 are 2, 19, 179. Prime factorization of 27208 in exponential form is:

27208 = 2³ × 19¹ × 179¹

Step-2: Prime Factorization of 27214

Prime factors of 27214 are 2, 11, 1237. Prime factorization of 27214 in exponential form is:

27214 = 2¹ × 11¹ × 1237¹

Step-3: Factors of 27208

List of positive integer factors of 27208 that divides 27208 without a remainder.

1, 2, 4, 8, 19, 38, 76, 152, 179, 358, 716, 1432, 3401, 6802, 13604

Step-4: Factors of 27214

List of positive integer factors of 27214 that divides 27208 without a remainder.

1, 2, 11, 22, 1237, 2474, 13607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27208 and 27214. The biggest common factor number is the GCF number.
So the greatest common factor 27208 and 27214 is 2.

Also check out the Least Common Multiple of 27208 and 27214