What is the Greatest Common Factor of 38760 and 38772?

Greatest common factor (GCF) of 38760 and 38772 is 12.

GCF(38760,38772) = 12

We will now calculate the prime factors of 38760 and 38772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38760 and 38772.

How to find the GCF of 38760 and 38772?

We will first find the prime factorization of 38760 and 38772. After we will calculate the factors of 38760 and 38772 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 38772

Prime factors of 38772 are 2, 3, 359. Prime factorization of 38772 in exponential form is:

38772 = 2² × 3³ × 359¹

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 38772

List of positive integer factors of 38772 that divides 38760 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 359, 718, 1077, 1436, 2154, 3231, 4308, 6462, 9693, 12924, 19386

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38760 and 38772. The biggest common factor number is the GCF number.
So the greatest common factor 38760 and 38772 is 12.

Also check out the Least Common Multiple of 38760 and 38772