What is the Greatest Common Factor of 27945 and 27960?

Greatest common factor (GCF) of 27945 and 27960 is 15.

GCF(27945,27960) = 15

We will now calculate the prime factors of 27945 and 27960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27945 and 27960.

How to find the GCF of 27945 and 27960?

We will first find the prime factorization of 27945 and 27960. After we will calculate the factors of 27945 and 27960 and find the biggest common factor number .

Step-1: Prime Factorization of 27945

Prime factors of 27945 are 3, 5, 23. Prime factorization of 27945 in exponential form is:

27945 = 3⁵ × 5¹ × 23¹

Step-2: Prime Factorization of 27960

Prime factors of 27960 are 2, 3, 5, 233. Prime factorization of 27960 in exponential form is:

27960 = 2³ × 3¹ × 5¹ × 233¹

Step-3: Factors of 27945

List of positive integer factors of 27945 that divides 27945 without a remainder.

1, 3, 5, 9, 15, 23, 27, 45, 69, 81, 115, 135, 207, 243, 345, 405, 621, 1035, 1215, 1863, 3105, 5589, 9315

Step-4: Factors of 27960

List of positive integer factors of 27960 that divides 27945 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 233, 466, 699, 932, 1165, 1398, 1864, 2330, 2796, 3495, 4660, 5592, 6990, 9320, 13980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27945 and 27960. The biggest common factor number is the GCF number.
So the greatest common factor 27945 and 27960 is 15.

Also check out the Least Common Multiple of 27945 and 27960