What is the Greatest Common Factor of 9205 and 9214?

Greatest common factor (GCF) of 9205 and 9214 is 1.

GCF(9205,9214) = 1

We will now calculate the prime factors of 9205 and 9214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9205 and 9214.

How to find the GCF of 9205 and 9214?

We will first find the prime factorization of 9205 and 9214. After we will calculate the factors of 9205 and 9214 and find the biggest common factor number .

Step-1: Prime Factorization of 9205

Prime factors of 9205 are 5, 7, 263. Prime factorization of 9205 in exponential form is:

9205 = 5¹ × 7¹ × 263¹

Step-2: Prime Factorization of 9214

Prime factors of 9214 are 2, 17, 271. Prime factorization of 9214 in exponential form is:

9214 = 2¹ × 17¹ × 271¹

Step-3: Factors of 9205

List of positive integer factors of 9205 that divides 9205 without a remainder.

1, 5, 7, 35, 263, 1315, 1841

Step-4: Factors of 9214

List of positive integer factors of 9214 that divides 9205 without a remainder.

1, 2, 17, 34, 271, 542, 4607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9205 and 9214. The biggest common factor number is the GCF number.
So the greatest common factor 9205 and 9214 is 1.

Also check out the Least Common Multiple of 9205 and 9214