What is the Greatest Common Factor of 30300 and 30315?

Greatest common factor (GCF) of 30300 and 30315 is 15.

GCF(30300,30315) = 15

We will now calculate the prime factors of 30300 and 30315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30300 and 30315.

How to find the GCF of 30300 and 30315?

We will first find the prime factorization of 30300 and 30315. After we will calculate the factors of 30300 and 30315 and find the biggest common factor number .

Step-1: Prime Factorization of 30300

Prime factors of 30300 are 2, 3, 5, 101. Prime factorization of 30300 in exponential form is:

30300 = 2² × 3¹ × 5² × 101¹

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 30300

List of positive integer factors of 30300 that divides 30300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 101, 150, 202, 300, 303, 404, 505, 606, 1010, 1212, 1515, 2020, 2525, 3030, 5050, 6060, 7575, 10100, 15150

Step-4: Factors of 30315

List of positive integer factors of 30315 that divides 30300 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 30300 and 30315. The biggest common factor number is the GCF number.
So the greatest common factor 30300 and 30315 is 15.

Also check out the Least Common Multiple of 30300 and 30315