What is the Greatest Common Factor of 77745 and 77760?

Greatest common factor (GCF) of 77745 and 77760 is 15.

GCF(77745,77760) = 15

We will now calculate the prime factors of 77745 and 77760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77745 and 77760.

How to find the GCF of 77745 and 77760?

We will first find the prime factorization of 77745 and 77760. After we will calculate the factors of 77745 and 77760 and find the biggest common factor number .

Step-1: Prime Factorization of 77745

Prime factors of 77745 are 3, 5, 71, 73. Prime factorization of 77745 in exponential form is:

77745 = 3¹ × 5¹ × 71¹ × 73¹

Step-2: Prime Factorization of 77760

Prime factors of 77760 are 2, 3, 5. Prime factorization of 77760 in exponential form is:

77760 = 2⁶ × 3⁵ × 5¹

Step-3: Factors of 77745

List of positive integer factors of 77745 that divides 77745 without a remainder.

1, 3, 5, 15, 71, 73, 213, 219, 355, 365, 1065, 1095, 5183, 15549, 25915

Step-4: Factors of 77760

List of positive integer factors of 77760 that divides 77745 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 192, 216, 240, 243, 270, 288, 320, 324, 360, 405, 432, 480, 486, 540, 576, 648, 720, 810, 864, 960, 972, 1080, 1215, 1296, 1440, 1620, 1728, 1944, 2160, 2430, 2592, 2880, 3240, 3888, 4320, 4860, 5184, 6480, 7776, 8640, 9720, 12960, 15552, 19440, 25920, 38880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77745 and 77760. The biggest common factor number is the GCF number.
So the greatest common factor 77745 and 77760 is 15.

Also check out the Least Common Multiple of 77745 and 77760