What is the Greatest Common Factor of 38740 and 38760?

Greatest common factor (GCF) of 38740 and 38760 is 20.

GCF(38740,38760) = 20

We will now calculate the prime factors of 38740 and 38760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38740 and 38760.

How to find the GCF of 38740 and 38760?

We will first find the prime factorization of 38740 and 38760. After we will calculate the factors of 38740 and 38760 and find the biggest common factor number .

Step-1: Prime Factorization of 38740

Prime factors of 38740 are 2, 5, 13, 149. Prime factorization of 38740 in exponential form is:

38740 = 2² × 5¹ × 13¹ × 149¹

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 38740

List of positive integer factors of 38740 that divides 38740 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 149, 260, 298, 596, 745, 1490, 1937, 2980, 3874, 7748, 9685, 19370

Step-4: Factors of 38760

List of positive integer factors of 38760 that divides 38740 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 38740 and 38760. The biggest common factor number is the GCF number.
So the greatest common factor 38740 and 38760 is 20.

Also check out the Least Common Multiple of 38740 and 38760