What is the Greatest Common Factor of 38745 and 38760?

Greatest common factor (GCF) of 38745 and 38760 is 15.

GCF(38745,38760) = 15

We will now calculate the prime factors of 38745 and 38760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38745 and 38760.

How to find the GCF of 38745 and 38760?

We will first find the prime factorization of 38745 and 38760. After we will calculate the factors of 38745 and 38760 and find the biggest common factor number .

Step-1: Prime Factorization of 38745

Prime factors of 38745 are 3, 5, 7, 41. Prime factorization of 38745 in exponential form is:

38745 = 3³ × 5¹ × 7¹ × 41¹

Step-2: 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-3: Factors of 38745

List of positive integer factors of 38745 that divides 38745 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 41, 45, 63, 105, 123, 135, 189, 205, 287, 315, 369, 615, 861, 945, 1107, 1435, 1845, 2583, 4305, 5535, 7749, 12915

Step-4: Factors of 38760

List of positive integer factors of 38760 that divides 38745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38745 and 38760. The biggest common factor number is the GCF number.
So the greatest common factor 38745 and 38760 is 15.

Also check out the Least Common Multiple of 38745 and 38760