What is the Greatest Common Factor of 48314 and 48320?

Greatest common factor (GCF) of 48314 and 48320 is 2.

GCF(48314,48320) = 2

We will now calculate the prime factors of 48314 and 48320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48314 and 48320.

How to find the GCF of 48314 and 48320?

We will first find the prime factorization of 48314 and 48320. After we will calculate the factors of 48314 and 48320 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 48320

Prime factors of 48320 are 2, 5, 151. Prime factorization of 48320 in exponential form is:

48320 = 2⁶ × 5¹ × 151¹

Step-3: Factors of 48314

List of positive integer factors of 48314 that divides 48314 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

Step-4: Factors of 48320

List of positive integer factors of 48320 that divides 48314 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 151, 160, 302, 320, 604, 755, 1208, 1510, 2416, 3020, 4832, 6040, 9664, 12080, 24160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48314 and 48320. The biggest common factor number is the GCF number.
So the greatest common factor 48314 and 48320 is 2.

Also check out the Least Common Multiple of 48314 and 48320