What is the Greatest Common Factor of 30510 and 30528?

Greatest common factor (GCF) of 30510 and 30528 is 18.

GCF(30510,30528) = 18

We will now calculate the prime factors of 30510 and 30528, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30510 and 30528.

How to find the GCF of 30510 and 30528?

We will first find the prime factorization of 30510 and 30528. After we will calculate the factors of 30510 and 30528 and find the biggest common factor number .

Step-1: Prime Factorization of 30510

Prime factors of 30510 are 2, 3, 5, 113. Prime factorization of 30510 in exponential form is:

30510 = 2¹ × 3³ × 5¹ × 113¹

Step-2: 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-3: Factors of 30510

List of positive integer factors of 30510 that divides 30510 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 113, 135, 226, 270, 339, 565, 678, 1017, 1130, 1695, 2034, 3051, 3390, 5085, 6102, 10170, 15255

Step-4: Factors of 30528

List of positive integer factors of 30528 that divides 30510 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30510 and 30528. The biggest common factor number is the GCF number.
So the greatest common factor 30510 and 30528 is 18.

Also check out the Least Common Multiple of 30510 and 30528