What is the Greatest Common Factor of 2214 and 2233?

Greatest common factor (GCF) of 2214 and 2233 is 1.

GCF(2214,2233) = 1

We will now calculate the prime factors of 2214 and 2233, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2214 and 2233.

How to find the GCF of 2214 and 2233?

We will first find the prime factorization of 2214 and 2233. After we will calculate the factors of 2214 and 2233 and find the biggest common factor number .

Step-1: Prime Factorization of 2214

Prime factors of 2214 are 2, 3, 41. Prime factorization of 2214 in exponential form is:

2214 = 2¹ × 3³ × 41¹

Step-2: Prime Factorization of 2233

Prime factors of 2233 are 7, 11, 29. Prime factorization of 2233 in exponential form is:

2233 = 7¹ × 11¹ × 29¹

Step-3: Factors of 2214

List of positive integer factors of 2214 that divides 2214 without a remainder.

1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107

Step-4: Factors of 2233

List of positive integer factors of 2233 that divides 2214 without a remainder.

1, 7, 11, 29, 77, 203, 319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2214 and 2233. The biggest common factor number is the GCF number.
So the greatest common factor 2214 and 2233 is 1.

Also check out the Least Common Multiple of 2214 and 2233