What is the Greatest Common Factor of 38760 and 38780?

Greatest common factor (GCF) of 38760 and 38780 is 20.

GCF(38760,38780) = 20

We will now calculate the prime factors of 38760 and 38780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38760 and 38780.

How to find the GCF of 38760 and 38780?

We will first find the prime factorization of 38760 and 38780. After we will calculate the factors of 38760 and 38780 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 38780

Prime factors of 38780 are 2, 5, 7, 277. Prime factorization of 38780 in exponential form is:

38780 = 2² × 5¹ × 7¹ × 277¹

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 38780

List of positive integer factors of 38780 that divides 38760 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 277, 554, 1108, 1385, 1939, 2770, 3878, 5540, 7756, 9695, 19390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38760 and 38780. The biggest common factor number is the GCF number.
So the greatest common factor 38760 and 38780 is 20.

Also check out the Least Common Multiple of 38760 and 38780