What is the Greatest Common Factor of 30500 and 30506?

Greatest common factor (GCF) of 30500 and 30506 is 2.

GCF(30500,30506) = 2

We will now calculate the prime factors of 30500 and 30506, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30500 and 30506.

How to find the GCF of 30500 and 30506?

We will first find the prime factorization of 30500 and 30506. After we will calculate the factors of 30500 and 30506 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 30506

Prime factors of 30506 are 2, 7, 2179. Prime factorization of 30506 in exponential form is:

30506 = 2¹ × 7¹ × 2179¹

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 30506

List of positive integer factors of 30506 that divides 30500 without a remainder.

1, 2, 7, 14, 2179, 4358, 15253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30500 and 30506. The biggest common factor number is the GCF number.
So the greatest common factor 30500 and 30506 is 2.

Also check out the Least Common Multiple of 30500 and 30506