What is the Greatest Common Factor of 48306 and 48314?

Greatest common factor (GCF) of 48306 and 48314 is 2.

GCF(48306,48314) = 2

We will now calculate the prime factors of 48306 and 48314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48306 and 48314.

How to find the GCF of 48306 and 48314?

We will first find the prime factorization of 48306 and 48314. After we will calculate the factors of 48306 and 48314 and find the biggest common factor number .

Step-1: Prime Factorization of 48306

Prime factors of 48306 are 2, 3, 83, 97. Prime factorization of 48306 in exponential form is:

48306 = 2¹ × 3¹ × 83¹ × 97¹

Step-2: Prime Factorization of 48314

Prime factors of 48314 are 2, 7, 17, 29. Prime factorization of 48314 in exponential form is:

48314 = 2¹ × 7² × 17¹ × 29¹

Step-3: Factors of 48306

List of positive integer factors of 48306 that divides 48306 without a remainder.

1, 2, 3, 6, 83, 97, 166, 194, 249, 291, 498, 582, 8051, 16102, 24153

Step-4: Factors of 48314

List of positive integer factors of 48314 that divides 48306 without a remainder.

1, 2, 7, 14, 17, 29, 34, 49, 58, 98, 119, 203, 238, 406, 493, 833, 986, 1421, 1666, 2842, 3451, 6902, 24157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48306 and 48314. The biggest common factor number is the GCF number.
So the greatest common factor 48306 and 48314 is 2.

Also check out the Least Common Multiple of 48306 and 48314