What is the Greatest Common Factor of 30205 and 30219?

Greatest common factor (GCF) of 30205 and 30219 is 7.

GCF(30205,30219) = 7

We will now calculate the prime factors of 30205 and 30219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30205 and 30219.

How to find the GCF of 30205 and 30219?

We will first find the prime factorization of 30205 and 30219. After we will calculate the factors of 30205 and 30219 and find the biggest common factor number .

Step-1: Prime Factorization of 30205

Prime factors of 30205 are 5, 7, 863. Prime factorization of 30205 in exponential form is:

30205 = 5¹ × 7¹ × 863¹

Step-2: 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-3: Factors of 30205

List of positive integer factors of 30205 that divides 30205 without a remainder.

1, 5, 7, 35, 863, 4315, 6041

Step-4: Factors of 30219

List of positive integer factors of 30219 that divides 30205 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30205 and 30219. The biggest common factor number is the GCF number.
So the greatest common factor 30205 and 30219 is 7.

Also check out the Least Common Multiple of 30205 and 30219