What is the Greatest Common Factor of 30825 and 30830?

Greatest common factor (GCF) of 30825 and 30830 is 5.

GCF(30825,30830) = 5

We will now calculate the prime factors of 30825 and 30830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30825 and 30830.

How to find the GCF of 30825 and 30830?

We will first find the prime factorization of 30825 and 30830. After we will calculate the factors of 30825 and 30830 and find the biggest common factor number .

Step-1: Prime Factorization of 30825

Prime factors of 30825 are 3, 5, 137. Prime factorization of 30825 in exponential form is:

30825 = 3² × 5² × 137¹

Step-2: Prime Factorization of 30830

Prime factors of 30830 are 2, 5, 3083. Prime factorization of 30830 in exponential form is:

30830 = 2¹ × 5¹ × 3083¹

Step-3: Factors of 30825

List of positive integer factors of 30825 that divides 30825 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 137, 225, 411, 685, 1233, 2055, 3425, 6165, 10275

Step-4: Factors of 30830

List of positive integer factors of 30830 that divides 30825 without a remainder.

1, 2, 5, 10, 3083, 6166, 15415

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30825 and 30830. The biggest common factor number is the GCF number.
So the greatest common factor 30825 and 30830 is 5.

Also check out the Least Common Multiple of 30825 and 30830