What is the Greatest Common Factor of 30272 and 30288?

Greatest common factor (GCF) of 30272 and 30288 is 16.

GCF(30272,30288) = 16

We will now calculate the prime factors of 30272 and 30288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30272 and 30288.

How to find the GCF of 30272 and 30288?

We will first find the prime factorization of 30272 and 30288. After we will calculate the factors of 30272 and 30288 and find the biggest common factor number .

Step-1: Prime Factorization of 30272

Prime factors of 30272 are 2, 11, 43. Prime factorization of 30272 in exponential form is:

30272 = 2⁶ × 11¹ × 43¹

Step-2: 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-3: Factors of 30272

List of positive integer factors of 30272 that divides 30272 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 43, 44, 64, 86, 88, 172, 176, 344, 352, 473, 688, 704, 946, 1376, 1892, 2752, 3784, 7568, 15136

Step-4: Factors of 30288

List of positive integer factors of 30288 that divides 30272 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30272 and 30288. The biggest common factor number is the GCF number.
So the greatest common factor 30272 and 30288 is 16.

Also check out the Least Common Multiple of 30272 and 30288