What is the Greatest Common Factor of 21205 and 21225?

Greatest common factor (GCF) of 21205 and 21225 is 5.

GCF(21205,21225) = 5

We will now calculate the prime factors of 21205 and 21225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21205 and 21225.

How to find the GCF of 21205 and 21225?

We will first find the prime factorization of 21205 and 21225. After we will calculate the factors of 21205 and 21225 and find the biggest common factor number .

Step-1: Prime Factorization of 21205

Prime factors of 21205 are 5, 4241. Prime factorization of 21205 in exponential form is:

21205 = 5¹ × 4241¹

Step-2: Prime Factorization of 21225

Prime factors of 21225 are 3, 5, 283. Prime factorization of 21225 in exponential form is:

21225 = 3¹ × 5² × 283¹

Step-3: Factors of 21205

List of positive integer factors of 21205 that divides 21205 without a remainder.

1, 5, 4241

Step-4: Factors of 21225

List of positive integer factors of 21225 that divides 21205 without a remainder.

1, 3, 5, 15, 25, 75, 283, 849, 1415, 4245, 7075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21205 and 21225. The biggest common factor number is the GCF number.
So the greatest common factor 21205 and 21225 is 5.

Also check out the Least Common Multiple of 21205 and 21225