What is the Greatest Common Factor of 30288 and 30304?

Greatest common factor (GCF) of 30288 and 30304 is 16.

GCF(30288,30304) = 16

We will now calculate the prime factors of 30288 and 30304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30288 and 30304.

How to find the GCF of 30288 and 30304?

We will first find the prime factorization of 30288 and 30304. After we will calculate the factors of 30288 and 30304 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 30304

Prime factors of 30304 are 2, 947. Prime factorization of 30304 in exponential form is:

30304 = 2⁵ × 947¹

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 30304

List of positive integer factors of 30304 that divides 30288 without a remainder.

1, 2, 4, 8, 16, 32, 947, 1894, 3788, 7576, 15152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30288 and 30304. The biggest common factor number is the GCF number.
So the greatest common factor 30288 and 30304 is 16.

Also check out the Least Common Multiple of 30288 and 30304