What is the Greatest Common Factor of 30360 and 30375?

Greatest common factor (GCF) of 30360 and 30375 is 15.

GCF(30360,30375) = 15

We will now calculate the prime factors of 30360 and 30375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30360 and 30375.

How to find the GCF of 30360 and 30375?

We will first find the prime factorization of 30360 and 30375. After we will calculate the factors of 30360 and 30375 and find the biggest common factor number .

Step-1: Prime Factorization of 30360

Prime factors of 30360 are 2, 3, 5, 11, 23. Prime factorization of 30360 in exponential form is:

30360 = 2³ × 3¹ × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 30375

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

30375 = 3⁵ × 5³

Step-3: Factors of 30360

List of positive integer factors of 30360 that divides 30360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 23, 24, 30, 33, 40, 44, 46, 55, 60, 66, 69, 88, 92, 110, 115, 120, 132, 138, 165, 184, 220, 230, 253, 264, 276, 330, 345, 440, 460, 506, 552, 660, 690, 759, 920, 1012, 1265, 1320, 1380, 1518, 2024, 2530, 2760, 3036, 3795, 5060, 6072, 7590, 10120, 15180

Step-4: Factors of 30375

List of positive integer factors of 30375 that divides 30360 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30360 and 30375. The biggest common factor number is the GCF number.
So the greatest common factor 30360 and 30375 is 15.

Also check out the Least Common Multiple of 30360 and 30375