What is the Greatest Common Factor of 30258 and 30272?

Greatest common factor (GCF) of 30258 and 30272 is 2.

GCF(30258,30272) = 2

We will now calculate the prime factors of 30258 and 30272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30258 and 30272.

How to find the GCF of 30258 and 30272?

We will first find the prime factorization of 30258 and 30272. After we will calculate the factors of 30258 and 30272 and find the biggest common factor number .

Step-1: Prime Factorization of 30258

Prime factors of 30258 are 2, 3, 41. Prime factorization of 30258 in exponential form is:

30258 = 2¹ × 3² × 41²

Step-2: 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-3: Factors of 30258

List of positive integer factors of 30258 that divides 30258 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738, 1681, 3362, 5043, 10086, 15129

Step-4: Factors of 30272

List of positive integer factors of 30272 that divides 30258 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30258 and 30272. The biggest common factor number is the GCF number.
So the greatest common factor 30258 and 30272 is 2.

Also check out the Least Common Multiple of 30258 and 30272