What is the Greatest Common Factor of 21810 and 21825?

Greatest common factor (GCF) of 21810 and 21825 is 15.

GCF(21810,21825) = 15

We will now calculate the prime factors of 21810 and 21825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21810 and 21825.

How to find the GCF of 21810 and 21825?

We will first find the prime factorization of 21810 and 21825. After we will calculate the factors of 21810 and 21825 and find the biggest common factor number .

Step-1: Prime Factorization of 21810

Prime factors of 21810 are 2, 3, 5, 727. Prime factorization of 21810 in exponential form is:

21810 = 2¹ × 3¹ × 5¹ × 727¹

Step-2: 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-3: Factors of 21810

List of positive integer factors of 21810 that divides 21810 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 727, 1454, 2181, 3635, 4362, 7270, 10905

Step-4: Factors of 21825

List of positive integer factors of 21825 that divides 21810 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21810 and 21825. The biggest common factor number is the GCF number.
So the greatest common factor 21810 and 21825 is 15.

Also check out the Least Common Multiple of 21810 and 21825