What is the Greatest Common Factor of 27930 and 27945?

Greatest common factor (GCF) of 27930 and 27945 is 15.

GCF(27930,27945) = 15

We will now calculate the prime factors of 27930 and 27945, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27930 and 27945.

How to find the GCF of 27930 and 27945?

We will first find the prime factorization of 27930 and 27945. After we will calculate the factors of 27930 and 27945 and find the biggest common factor number .

Step-1: Prime Factorization of 27930

Prime factors of 27930 are 2, 3, 5, 7, 19. Prime factorization of 27930 in exponential form is:

27930 = 2¹ × 3¹ × 5¹ × 7² × 19¹

Step-2: 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-3: Factors of 27930

List of positive integer factors of 27930 that divides 27930 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 30, 35, 38, 42, 49, 57, 70, 95, 98, 105, 114, 133, 147, 190, 210, 245, 266, 285, 294, 399, 490, 570, 665, 735, 798, 931, 1330, 1470, 1862, 1995, 2793, 3990, 4655, 5586, 9310, 13965

Step-4: Factors of 27945

List of positive integer factors of 27945 that divides 27930 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27930 and 27945. The biggest common factor number is the GCF number.
So the greatest common factor 27930 and 27945 is 15.

Also check out the Least Common Multiple of 27930 and 27945