What is the Greatest Common Factor of 21808 and 21825?

Greatest common factor (GCF) of 21808 and 21825 is 1.

GCF(21808,21825) = 1

We will now calculate the prime factors of 21808 and 21825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21808 and 21825.

How to find the GCF of 21808 and 21825?

We will first find the prime factorization of 21808 and 21825. After we will calculate the factors of 21808 and 21825 and find the biggest common factor number .

Step-1: Prime Factorization of 21808

Prime factors of 21808 are 2, 29, 47. Prime factorization of 21808 in exponential form is:

21808 = 2⁴ × 29¹ × 47¹

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 21808

List of positive integer factors of 21808 that divides 21808 without a remainder.

1, 2, 4, 8, 16, 29, 47, 58, 94, 116, 188, 232, 376, 464, 752, 1363, 2726, 5452, 10904

Step-4: Factors of 21825

List of positive integer factors of 21825 that divides 21808 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 21808 and 21825. The biggest common factor number is the GCF number.
So the greatest common factor 21808 and 21825 is 1.

Also check out the Least Common Multiple of 21808 and 21825