What is the Greatest Common Factor of 30305 and 30315?

Greatest common factor (GCF) of 30305 and 30315 is 5.

GCF(30305,30315) = 5

We will now calculate the prime factors of 30305 and 30315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30305 and 30315.

How to find the GCF of 30305 and 30315?

We will first find the prime factorization of 30305 and 30315. After we will calculate the factors of 30305 and 30315 and find the biggest common factor number .

Step-1: Prime Factorization of 30305

Prime factors of 30305 are 5, 11, 19, 29. Prime factorization of 30305 in exponential form is:

30305 = 5¹ × 11¹ × 19¹ × 29¹

Step-2: Prime Factorization of 30315

Prime factors of 30315 are 3, 5, 43, 47. Prime factorization of 30315 in exponential form is:

30315 = 3¹ × 5¹ × 43¹ × 47¹

Step-3: Factors of 30305

List of positive integer factors of 30305 that divides 30305 without a remainder.

1, 5, 11, 19, 29, 55, 95, 145, 209, 319, 551, 1045, 1595, 2755, 6061

Step-4: Factors of 30315

List of positive integer factors of 30315 that divides 30305 without a remainder.

1, 3, 5, 15, 43, 47, 129, 141, 215, 235, 645, 705, 2021, 6063, 10105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30305 and 30315. The biggest common factor number is the GCF number.
So the greatest common factor 30305 and 30315 is 5.

Also check out the Least Common Multiple of 30305 and 30315