What is the Greatest Common Factor of 30225 and 30238?

Greatest common factor (GCF) of 30225 and 30238 is 13.

GCF(30225,30238) = 13

We will now calculate the prime factors of 30225 and 30238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30225 and 30238.

How to find the GCF of 30225 and 30238?

We will first find the prime factorization of 30225 and 30238. After we will calculate the factors of 30225 and 30238 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 30238

Prime factors of 30238 are 2, 13, 1163. Prime factorization of 30238 in exponential form is:

30238 = 2¹ × 13¹ × 1163¹

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 30238

List of positive integer factors of 30238 that divides 30225 without a remainder.

1, 2, 13, 26, 1163, 2326, 15119

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30225 and 30238. The biggest common factor number is the GCF number.
So the greatest common factor 30225 and 30238 is 13.

Also check out the Least Common Multiple of 30225 and 30238