What is the Greatest Common Factor of 213 and 225?

Greatest common factor (GCF) of 213 and 225 is 3.

GCF(213,225) = 3

We will now calculate the prime factors of 213 and 225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 213 and 225.

How to find the GCF of 213 and 225?

We will first find the prime factorization of 213 and 225. After we will calculate the factors of 213 and 225 and find the biggest common factor number .

Step-1: Prime Factorization of 213

Prime factors of 213 are 3, 71. Prime factorization of 213 in exponential form is:

213 = 3¹ × 71¹

Step-2: Prime Factorization of 225

Prime factors of 225 are 3, 5. Prime factorization of 225 in exponential form is:

225 = 3² × 5²

Step-3: Factors of 213

List of positive integer factors of 213 that divides 213 without a remainder.

1, 3, 71

Step-4: Factors of 225

List of positive integer factors of 225 that divides 213 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 213 and 225. The biggest common factor number is the GCF number.
So the greatest common factor 213 and 225 is 3.

Also check out the Least Common Multiple of 213 and 225