What is the Greatest Common Factor of 22288 and 22302?

Greatest common factor (GCF) of 22288 and 22302 is 14.

GCF(22288,22302) = 14

We will now calculate the prime factors of 22288 and 22302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22288 and 22302.

How to find the GCF of 22288 and 22302?

We will first find the prime factorization of 22288 and 22302. After we will calculate the factors of 22288 and 22302 and find the biggest common factor number .

Step-1: Prime Factorization of 22288

Prime factors of 22288 are 2, 7, 199. Prime factorization of 22288 in exponential form is:

22288 = 2⁴ × 7¹ × 199¹

Step-2: Prime Factorization of 22302

Prime factors of 22302 are 2, 3, 7, 59. Prime factorization of 22302 in exponential form is:

22302 = 2¹ × 3³ × 7¹ × 59¹

Step-3: Factors of 22288

List of positive integer factors of 22288 that divides 22288 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 199, 398, 796, 1393, 1592, 2786, 3184, 5572, 11144

Step-4: Factors of 22302

List of positive integer factors of 22302 that divides 22288 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 59, 63, 118, 126, 177, 189, 354, 378, 413, 531, 826, 1062, 1239, 1593, 2478, 3186, 3717, 7434, 11151

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22288 and 22302. The biggest common factor number is the GCF number.
So the greatest common factor 22288 and 22302 is 14.

Also check out the Least Common Multiple of 22288 and 22302