What is the Greatest Common Factor of 38760 and 38775?

Greatest common factor (GCF) of 38760 and 38775 is 15.

GCF(38760,38775) = 15

We will now calculate the prime factors of 38760 and 38775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38760 and 38775.

How to find the GCF of 38760 and 38775?

We will first find the prime factorization of 38760 and 38775. After we will calculate the factors of 38760 and 38775 and find the biggest common factor number .

Step-1: Prime Factorization of 38760

Prime factors of 38760 are 2, 3, 5, 17, 19. Prime factorization of 38760 in exponential form is:

38760 = 2³ × 3¹ × 5¹ × 17¹ × 19¹

Step-2: Prime Factorization of 38775

Prime factors of 38775 are 3, 5, 11, 47. Prime factorization of 38775 in exponential form is:

38775 = 3¹ × 5² × 11¹ × 47¹

Step-3: Factors of 38760

List of positive integer factors of 38760 that divides 38760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 19, 20, 24, 30, 34, 38, 40, 51, 57, 60, 68, 76, 85, 95, 102, 114, 120, 136, 152, 170, 190, 204, 228, 255, 285, 323, 340, 380, 408, 456, 510, 570, 646, 680, 760, 969, 1020, 1140, 1292, 1615, 1938, 2040, 2280, 2584, 3230, 3876, 4845, 6460, 7752, 9690, 12920, 19380

Step-4: Factors of 38775

List of positive integer factors of 38775 that divides 38760 without a remainder.

1, 3, 5, 11, 15, 25, 33, 47, 55, 75, 141, 165, 235, 275, 517, 705, 825, 1175, 1551, 2585, 3525, 7755, 12925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38760 and 38775. The biggest common factor number is the GCF number.
So the greatest common factor 38760 and 38775 is 15.

Also check out the Least Common Multiple of 38760 and 38775