What is the Greatest Common Factor of 2214 and 2223?

Greatest common factor (GCF) of 2214 and 2223 is 9.

GCF(2214,2223) = 9

We will now calculate the prime factors of 2214 and 2223, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2214 and 2223.

How to find the GCF of 2214 and 2223?

We will first find the prime factorization of 2214 and 2223. After we will calculate the factors of 2214 and 2223 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 2223

Prime factors of 2223 are 3, 13, 19. Prime factorization of 2223 in exponential form is:

2223 = 3² × 13¹ × 19¹

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 2223

List of positive integer factors of 2223 that divides 2214 without a remainder.

1, 3, 9, 13, 19, 39, 57, 117, 171, 247, 741

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2214 and 2223. The biggest common factor number is the GCF number.
So the greatest common factor 2214 and 2223 is 9.

Also check out the Least Common Multiple of 2214 and 2223