What is the Greatest Common Factor of 30225 and 30234?

Greatest common factor (GCF) of 30225 and 30234 is 3.

GCF(30225,30234) = 3

We will now calculate the prime factors of 30225 and 30234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30225 and 30234.

How to find the GCF of 30225 and 30234?

We will first find the prime factorization of 30225 and 30234. After we will calculate the factors of 30225 and 30234 and find the biggest common factor number .

Step-1: Prime Factorization of 30225

Prime factors of 30225 are 3, 5, 13, 31. Prime factorization of 30225 in exponential form is:

30225 = 3¹ × 5² × 13¹ × 31¹

Step-2: Prime Factorization of 30234

Prime factors of 30234 are 2, 3, 5039. Prime factorization of 30234 in exponential form is:

30234 = 2¹ × 3¹ × 5039¹

Step-3: Factors of 30225

List of positive integer factors of 30225 that divides 30225 without a remainder.

1, 3, 5, 13, 15, 25, 31, 39, 65, 75, 93, 155, 195, 325, 403, 465, 775, 975, 1209, 2015, 2325, 6045, 10075

Step-4: Factors of 30234

List of positive integer factors of 30234 that divides 30225 without a remainder.

1, 2, 3, 6, 5039, 10078, 15117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30225 and 30234. The biggest common factor number is the GCF number.
So the greatest common factor 30225 and 30234 is 3.

Also check out the Least Common Multiple of 30225 and 30234