What is the Greatest Common Factor of 30288 and 30294?

Greatest common factor (GCF) of 30288 and 30294 is 6.

GCF(30288,30294) = 6

We will now calculate the prime factors of 30288 and 30294, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30288 and 30294.

How to find the GCF of 30288 and 30294?

We will first find the prime factorization of 30288 and 30294. After we will calculate the factors of 30288 and 30294 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 30294

Prime factors of 30294 are 2, 3, 11, 17. Prime factorization of 30294 in exponential form is:

30294 = 2¹ × 3⁴ × 11¹ × 17¹

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 30294

List of positive integer factors of 30294 that divides 30288 without a remainder.

1, 2, 3, 6, 9, 11, 17, 18, 22, 27, 33, 34, 51, 54, 66, 81, 99, 102, 153, 162, 187, 198, 297, 306, 374, 459, 561, 594, 891, 918, 1122, 1377, 1683, 1782, 2754, 3366, 5049, 10098, 15147

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30288 and 30294. The biggest common factor number is the GCF number.
So the greatest common factor 30288 and 30294 is 6.

Also check out the Least Common Multiple of 30288 and 30294