What is the Greatest Common Factor of 217 and 231?

Greatest common factor (GCF) of 217 and 231 is 7.

GCF(217,231) = 7

We will now calculate the prime factors of 217 and 231, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 217 and 231.

How to find the GCF of 217 and 231?

We will first find the prime factorization of 217 and 231. After we will calculate the factors of 217 and 231 and find the biggest common factor number .

Step-1: Prime Factorization of 217

Prime factors of 217 are 7, 31. Prime factorization of 217 in exponential form is:

217 = 7¹ × 31¹

Step-2: Prime Factorization of 231

Prime factors of 231 are 3, 7, 11. Prime factorization of 231 in exponential form is:

231 = 3¹ × 7¹ × 11¹

Step-3: Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31

Step-4: Factors of 231

List of positive integer factors of 231 that divides 217 without a remainder.

1, 3, 7, 11, 21, 33, 77

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 217 and 231. The biggest common factor number is the GCF number.
So the greatest common factor 217 and 231 is 7.

Also check out the Least Common Multiple of 217 and 231