What is the Greatest Common Factor of 30496 and 30514?

Greatest common factor (GCF) of 30496 and 30514 is 2.

GCF(30496,30514) = 2

We will now calculate the prime factors of 30496 and 30514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30496 and 30514.

How to find the GCF of 30496 and 30514?

We will first find the prime factorization of 30496 and 30514. After we will calculate the factors of 30496 and 30514 and find the biggest common factor number .

Step-1: Prime Factorization of 30496

Prime factors of 30496 are 2, 953. Prime factorization of 30496 in exponential form is:

30496 = 2⁵ × 953¹

Step-2: Prime Factorization of 30514

Prime factors of 30514 are 2, 11, 19, 73. Prime factorization of 30514 in exponential form is:

30514 = 2¹ × 11¹ × 19¹ × 73¹

Step-3: Factors of 30496

List of positive integer factors of 30496 that divides 30496 without a remainder.

1, 2, 4, 8, 16, 32, 953, 1906, 3812, 7624, 15248

Step-4: Factors of 30514

List of positive integer factors of 30514 that divides 30496 without a remainder.

1, 2, 11, 19, 22, 38, 73, 146, 209, 418, 803, 1387, 1606, 2774, 15257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30496 and 30514. The biggest common factor number is the GCF number.
So the greatest common factor 30496 and 30514 is 2.

Also check out the Least Common Multiple of 30496 and 30514