What is the Greatest Common Factor of 30500 and 30514?

Greatest common factor (GCF) of 30500 and 30514 is 2.

GCF(30500,30514) = 2

We will now calculate the prime factors of 30500 and 30514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30500 and 30514.

How to find the GCF of 30500 and 30514?

We will first find the prime factorization of 30500 and 30514. After we will calculate the factors of 30500 and 30514 and find the biggest common factor number .

Step-1: Prime Factorization of 30500

Prime factors of 30500 are 2, 5, 61. Prime factorization of 30500 in exponential form is:

30500 = 2² × 5³ × 61¹

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 30500

List of positive integer factors of 30500 that divides 30500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 61, 100, 122, 125, 244, 250, 305, 500, 610, 1220, 1525, 3050, 6100, 7625, 15250

Step-4: Factors of 30514

List of positive integer factors of 30514 that divides 30500 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 30500 and 30514. The biggest common factor number is the GCF number.
So the greatest common factor 30500 and 30514 is 2.

Also check out the Least Common Multiple of 30500 and 30514