What is the Greatest Common Factor of 11214 and 11232?

Greatest common factor (GCF) of 11214 and 11232 is 18.

GCF(11214,11232) = 18

We will now calculate the prime factors of 11214 and 11232, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11214 and 11232.

How to find the GCF of 11214 and 11232?

We will first find the prime factorization of 11214 and 11232. After we will calculate the factors of 11214 and 11232 and find the biggest common factor number .

Step-1: Prime Factorization of 11214

Prime factors of 11214 are 2, 3, 7, 89. Prime factorization of 11214 in exponential form is:

11214 = 2¹ × 3² × 7¹ × 89¹

Step-2: Prime Factorization of 11232

Prime factors of 11232 are 2, 3, 13. Prime factorization of 11232 in exponential form is:

11232 = 2⁵ × 3³ × 13¹

Step-3: Factors of 11214

List of positive integer factors of 11214 that divides 11214 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 89, 126, 178, 267, 534, 623, 801, 1246, 1602, 1869, 3738, 5607

Step-4: Factors of 11232

List of positive integer factors of 11232 that divides 11214 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 32, 36, 39, 48, 52, 54, 72, 78, 96, 104, 108, 117, 144, 156, 208, 216, 234, 288, 312, 351, 416, 432, 468, 624, 702, 864, 936, 1248, 1404, 1872, 2808, 3744, 5616

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11214 and 11232. The biggest common factor number is the GCF number.
So the greatest common factor 11214 and 11232 is 18.

Also check out the Least Common Multiple of 11214 and 11232