What is the Greatest Common Factor of 16275 and 16289?

Greatest common factor (GCF) of 16275 and 16289 is 7.

GCF(16275,16289) = 7

We will now calculate the prime factors of 16275 and 16289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16275 and 16289.

How to find the GCF of 16275 and 16289?

We will first find the prime factorization of 16275 and 16289. After we will calculate the factors of 16275 and 16289 and find the biggest common factor number .

Step-1: Prime Factorization of 16275

Prime factors of 16275 are 3, 5, 7, 31. Prime factorization of 16275 in exponential form is:

16275 = 3¹ × 5² × 7¹ × 31¹

Step-2: 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-3: Factors of 16275

List of positive integer factors of 16275 that divides 16275 without a remainder.

1, 3, 5, 7, 15, 21, 25, 31, 35, 75, 93, 105, 155, 175, 217, 465, 525, 651, 775, 1085, 2325, 3255, 5425

Step-4: Factors of 16289

List of positive integer factors of 16289 that divides 16275 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16275 and 16289. The biggest common factor number is the GCF number.
So the greatest common factor 16275 and 16289 is 7.

Also check out the Least Common Multiple of 16275 and 16289