What is the Greatest Common Factor of 16289 and 16302?

Greatest common factor (GCF) of 16289 and 16302 is 13.

GCF(16289,16302) = 13

We will now calculate the prime factors of 16289 and 16302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16289 and 16302.

How to find the GCF of 16289 and 16302?

We will first find the prime factorization of 16289 and 16302. After we will calculate the factors of 16289 and 16302 and find the biggest common factor number .

Step-1: Prime Factorization of 16289

Prime factors of 16289 are 7, 13, 179. Prime factorization of 16289 in exponential form is:

16289 = 7¹ × 13¹ × 179¹

Step-2: Prime Factorization of 16302

Prime factors of 16302 are 2, 3, 11, 13, 19. Prime factorization of 16302 in exponential form is:

16302 = 2¹ × 3¹ × 11¹ × 13¹ × 19¹

Step-3: Factors of 16289

List of positive integer factors of 16289 that divides 16289 without a remainder.

1, 7, 13, 91, 179, 1253, 2327

Step-4: Factors of 16302

List of positive integer factors of 16302 that divides 16289 without a remainder.

1, 2, 3, 6, 11, 13, 19, 22, 26, 33, 38, 39, 57, 66, 78, 114, 143, 209, 247, 286, 418, 429, 494, 627, 741, 858, 1254, 1482, 2717, 5434, 8151

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16289 and 16302. The biggest common factor number is the GCF number.
So the greatest common factor 16289 and 16302 is 13.

Also check out the Least Common Multiple of 16289 and 16302