What is the Greatest Common Factor of 15309 and 15323?

Greatest common factor (GCF) of 15309 and 15323 is 7.

GCF(15309,15323) = 7

We will now calculate the prime factors of 15309 and 15323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15309 and 15323.

How to find the GCF of 15309 and 15323?

We will first find the prime factorization of 15309 and 15323. After we will calculate the factors of 15309 and 15323 and find the biggest common factor number .

Step-1: Prime Factorization of 15309

Prime factors of 15309 are 3, 7. Prime factorization of 15309 in exponential form is:

15309 = 3⁷ × 7¹

Step-2: Prime Factorization of 15323

Prime factors of 15323 are 7, 11, 199. Prime factorization of 15323 in exponential form is:

15323 = 7¹ × 11¹ × 199¹

Step-3: Factors of 15309

List of positive integer factors of 15309 that divides 15309 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 729, 1701, 2187, 5103

Step-4: Factors of 15323

List of positive integer factors of 15323 that divides 15309 without a remainder.

1, 7, 11, 77, 199, 1393, 2189

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15309 and 15323. The biggest common factor number is the GCF number.
So the greatest common factor 15309 and 15323 is 7.

Also check out the Least Common Multiple of 15309 and 15323