What is the Greatest Common Factor of 30375 and 30384?

Greatest common factor (GCF) of 30375 and 30384 is 9.

GCF(30375,30384) = 9

We will now calculate the prime factors of 30375 and 30384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30375 and 30384.

How to find the GCF of 30375 and 30384?

We will first find the prime factorization of 30375 and 30384. After we will calculate the factors of 30375 and 30384 and find the biggest common factor number .

Step-1: Prime Factorization of 30375

Prime factors of 30375 are 3, 5. Prime factorization of 30375 in exponential form is:

30375 = 3⁵ × 5³

Step-2: Prime Factorization of 30384

Prime factors of 30384 are 2, 3, 211. Prime factorization of 30384 in exponential form is:

30384 = 2⁴ × 3² × 211¹

Step-3: Factors of 30375

List of positive integer factors of 30375 that divides 30375 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 375, 405, 675, 1125, 1215, 2025, 3375, 6075, 10125

Step-4: Factors of 30384

List of positive integer factors of 30384 that divides 30375 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 211, 422, 633, 844, 1266, 1688, 1899, 2532, 3376, 3798, 5064, 7596, 10128, 15192

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30375 and 30384. The biggest common factor number is the GCF number.
So the greatest common factor 30375 and 30384 is 9.

Also check out the Least Common Multiple of 30375 and 30384