What is the Greatest Common Factor of 30314 and 30320?

Greatest common factor (GCF) of 30314 and 30320 is 2.

GCF(30314,30320) = 2

We will now calculate the prime factors of 30314 and 30320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30314 and 30320.

How to find the GCF of 30314 and 30320?

We will first find the prime factorization of 30314 and 30320. After we will calculate the factors of 30314 and 30320 and find the biggest common factor number .

Step-1: Prime Factorization of 30314

Prime factors of 30314 are 2, 23, 659. Prime factorization of 30314 in exponential form is:

30314 = 2¹ × 23¹ × 659¹

Step-2: Prime Factorization of 30320

Prime factors of 30320 are 2, 5, 379. Prime factorization of 30320 in exponential form is:

30320 = 2⁴ × 5¹ × 379¹

Step-3: Factors of 30314

List of positive integer factors of 30314 that divides 30314 without a remainder.

1, 2, 23, 46, 659, 1318, 15157

Step-4: Factors of 30320

List of positive integer factors of 30320 that divides 30314 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 379, 758, 1516, 1895, 3032, 3790, 6064, 7580, 15160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30314 and 30320. The biggest common factor number is the GCF number.
So the greatest common factor 30314 and 30320 is 2.

Also check out the Least Common Multiple of 30314 and 30320