What is the Greatest Common Factor of 71760 and 71775?

Greatest common factor (GCF) of 71760 and 71775 is 15.

GCF(71760,71775) = 15

We will now calculate the prime factors of 71760 and 71775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71760 and 71775.

How to find the GCF of 71760 and 71775?

We will first find the prime factorization of 71760 and 71775. After we will calculate the factors of 71760 and 71775 and find the biggest common factor number .

Step-1: Prime Factorization of 71760

Prime factors of 71760 are 2, 3, 5, 13, 23. Prime factorization of 71760 in exponential form is:

71760 = 2⁴ × 3¹ × 5¹ × 13¹ × 23¹

Step-2: Prime Factorization of 71775

Prime factors of 71775 are 3, 5, 11, 29. Prime factorization of 71775 in exponential form is:

71775 = 3² × 5² × 11¹ × 29¹

Step-3: Factors of 71760

List of positive integer factors of 71760 that divides 71760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 23, 24, 26, 30, 39, 40, 46, 48, 52, 60, 65, 69, 78, 80, 92, 104, 115, 120, 130, 138, 156, 184, 195, 208, 230, 240, 260, 276, 299, 312, 345, 368, 390, 460, 520, 552, 598, 624, 690, 780, 897, 920, 1040, 1104, 1196, 1380, 1495, 1560, 1794, 1840, 2392, 2760, 2990, 3120, 3588, 4485, 4784, 5520, 5980, 7176, 8970, 11960, 14352, 17940, 23920, 35880

Step-4: Factors of 71775

List of positive integer factors of 71775 that divides 71760 without a remainder.

1, 3, 5, 9, 11, 15, 25, 29, 33, 45, 55, 75, 87, 99, 145, 165, 225, 261, 275, 319, 435, 495, 725, 825, 957, 1305, 1595, 2175, 2475, 2871, 4785, 6525, 7975, 14355, 23925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71760 and 71775. The biggest common factor number is the GCF number.
So the greatest common factor 71760 and 71775 is 15.

Also check out the Least Common Multiple of 71760 and 71775