What is the Greatest Common Factor of 30296 and 30314?

Greatest common factor (GCF) of 30296 and 30314 is 2.

GCF(30296,30314) = 2

We will now calculate the prime factors of 30296 and 30314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30296 and 30314.

How to find the GCF of 30296 and 30314?

We will first find the prime factorization of 30296 and 30314. After we will calculate the factors of 30296 and 30314 and find the biggest common factor number .

Step-1: Prime Factorization of 30296

Prime factors of 30296 are 2, 7, 541. Prime factorization of 30296 in exponential form is:

30296 = 2³ × 7¹ × 541¹

Step-2: 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-3: Factors of 30296

List of positive integer factors of 30296 that divides 30296 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 541, 1082, 2164, 3787, 4328, 7574, 15148

Step-4: Factors of 30314

List of positive integer factors of 30314 that divides 30296 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30296 and 30314. The biggest common factor number is the GCF number.
So the greatest common factor 30296 and 30314 is 2.

Also check out the Least Common Multiple of 30296 and 30314