What is the Greatest Common Factor of 21825 and 21830?

Greatest common factor (GCF) of 21825 and 21830 is 5.

GCF(21825,21830) = 5

We will now calculate the prime factors of 21825 and 21830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21825 and 21830.

How to find the GCF of 21825 and 21830?

We will first find the prime factorization of 21825 and 21830. After we will calculate the factors of 21825 and 21830 and find the biggest common factor number .

Step-1: Prime Factorization of 21825

Prime factors of 21825 are 3, 5, 97. Prime factorization of 21825 in exponential form is:

21825 = 3² × 5² × 97¹

Step-2: Prime Factorization of 21830

Prime factors of 21830 are 2, 5, 37, 59. Prime factorization of 21830 in exponential form is:

21830 = 2¹ × 5¹ × 37¹ × 59¹

Step-3: Factors of 21825

List of positive integer factors of 21825 that divides 21825 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 97, 225, 291, 485, 873, 1455, 2425, 4365, 7275

Step-4: Factors of 21830

List of positive integer factors of 21830 that divides 21825 without a remainder.

1, 2, 5, 10, 37, 59, 74, 118, 185, 295, 370, 590, 2183, 4366, 10915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21825 and 21830. The biggest common factor number is the GCF number.
So the greatest common factor 21825 and 21830 is 5.

Also check out the Least Common Multiple of 21825 and 21830