What is the Greatest Common Factor of 21825 and 21829?

Greatest common factor (GCF) of 21825 and 21829 is 1.

GCF(21825,21829) = 1

We will now calculate the prime factors of 21825 and 21829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21825 and 21829.

How to find the GCF of 21825 and 21829?

We will first find the prime factorization of 21825 and 21829. After we will calculate the factors of 21825 and 21829 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 21829

Prime factors of 21829 are 83, 263. Prime factorization of 21829 in exponential form is:

21829 = 83¹ × 263¹

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 21829

List of positive integer factors of 21829 that divides 21825 without a remainder.

1, 83, 263

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21825 and 21829. The biggest common factor number is the GCF number.
So the greatest common factor 21825 and 21829 is 1.

Also check out the Least Common Multiple of 21825 and 21829