What is the Greatest Common Factor of 77748 and 77760?

Greatest common factor (GCF) of 77748 and 77760 is 12.

GCF(77748,77760) = 12

We will now calculate the prime factors of 77748 and 77760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77748 and 77760.

How to find the GCF of 77748 and 77760?

We will first find the prime factorization of 77748 and 77760. After we will calculate the factors of 77748 and 77760 and find the biggest common factor number .

Step-1: Prime Factorization of 77748

Prime factors of 77748 are 2, 3, 11, 19, 31. Prime factorization of 77748 in exponential form is:

77748 = 2² × 3¹ × 11¹ × 19¹ × 31¹

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 77748

List of positive integer factors of 77748 that divides 77748 without a remainder.

1, 2, 3, 4, 6, 11, 12, 19, 22, 31, 33, 38, 44, 57, 62, 66, 76, 93, 114, 124, 132, 186, 209, 228, 341, 372, 418, 589, 627, 682, 836, 1023, 1178, 1254, 1364, 1767, 2046, 2356, 2508, 3534, 4092, 6479, 7068, 12958, 19437, 25916, 38874

Step-4: Factors of 77760

List of positive integer factors of 77760 that divides 77748 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 77748 and 77760. The biggest common factor number is the GCF number.
So the greatest common factor 77748 and 77760 is 12.

Also check out the Least Common Multiple of 77748 and 77760