What is the Greatest Common Factor of 30528 and 30540?

Greatest common factor (GCF) of 30528 and 30540 is 12.

GCF(30528,30540) = 12

We will now calculate the prime factors of 30528 and 30540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30528 and 30540.

How to find the GCF of 30528 and 30540?

We will first find the prime factorization of 30528 and 30540. After we will calculate the factors of 30528 and 30540 and find the biggest common factor number .

Step-1: Prime Factorization of 30528

Prime factors of 30528 are 2, 3, 53. Prime factorization of 30528 in exponential form is:

30528 = 2⁶ × 3² × 53¹

Step-2: Prime Factorization of 30540

Prime factors of 30540 are 2, 3, 5, 509. Prime factorization of 30540 in exponential form is:

30540 = 2² × 3¹ × 5¹ × 509¹

Step-3: Factors of 30528

List of positive integer factors of 30528 that divides 30528 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 53, 64, 72, 96, 106, 144, 159, 192, 212, 288, 318, 424, 477, 576, 636, 848, 954, 1272, 1696, 1908, 2544, 3392, 3816, 5088, 7632, 10176, 15264

Step-4: Factors of 30540

List of positive integer factors of 30540 that divides 30528 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 509, 1018, 1527, 2036, 2545, 3054, 5090, 6108, 7635, 10180, 15270

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30528 and 30540. The biggest common factor number is the GCF number.
So the greatest common factor 30528 and 30540 is 12.

Also check out the Least Common Multiple of 30528 and 30540