What is the Greatest Common Factor of 217 and 234?

Greatest common factor (GCF) of 217 and 234 is 1.

GCF(217,234) = 1

We will now calculate the prime factors of 217 and 234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 217 and 234.

How to find the GCF of 217 and 234?

We will first find the prime factorization of 217 and 234. After we will calculate the factors of 217 and 234 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 234

Prime factors of 234 are 2, 3, 13. Prime factorization of 234 in exponential form is:

234 = 2¹ × 3² × 13¹

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 234

List of positive integer factors of 234 that divides 217 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 217 and 234. The biggest common factor number is the GCF number.
So the greatest common factor 217 and 234 is 1.

Also check out the Least Common Multiple of 217 and 234