What is the Greatest Common Factor of 30288 and 30300?

Greatest common factor (GCF) of 30288 and 30300 is 12.

GCF(30288,30300) = 12

We will now calculate the prime factors of 30288 and 30300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30288 and 30300.

How to find the GCF of 30288 and 30300?

We will first find the prime factorization of 30288 and 30300. After we will calculate the factors of 30288 and 30300 and find the biggest common factor number .

Step-1: Prime Factorization of 30288

Prime factors of 30288 are 2, 3, 631. Prime factorization of 30288 in exponential form is:

30288 = 2⁴ × 3¹ × 631¹

Step-2: 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-3: Factors of 30288

List of positive integer factors of 30288 that divides 30288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 631, 1262, 1893, 2524, 3786, 5048, 7572, 10096, 15144

Step-4: Factors of 30300

List of positive integer factors of 30300 that divides 30288 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30288 and 30300. The biggest common factor number is the GCF number.
So the greatest common factor 30288 and 30300 is 12.

Also check out the Least Common Multiple of 30288 and 30300