What is the Greatest Common Factor of 30219 and 30225?

Greatest common factor (GCF) of 30219 and 30225 is 3.

GCF(30219,30225) = 3

We will now calculate the prime factors of 30219 and 30225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30219 and 30225.

How to find the GCF of 30219 and 30225?

We will first find the prime factorization of 30219 and 30225. After we will calculate the factors of 30219 and 30225 and find the biggest common factor number .

Step-1: Prime Factorization of 30219

Prime factors of 30219 are 3, 7, 1439. Prime factorization of 30219 in exponential form is:

30219 = 3¹ × 7¹ × 1439¹

Step-2: 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-3: Factors of 30219

List of positive integer factors of 30219 that divides 30219 without a remainder.

1, 3, 7, 21, 1439, 4317, 10073

Step-4: Factors of 30225

List of positive integer factors of 30225 that divides 30219 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30219 and 30225. The biggest common factor number is the GCF number.
So the greatest common factor 30219 and 30225 is 3.

Also check out the Least Common Multiple of 30219 and 30225