What is the Greatest Common Factor of 77760 and 77777?

Greatest common factor (GCF) of 77760 and 77777 is 1.

GCF(77760,77777) = 1

We will now calculate the prime factors of 77760 and 77777, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77760 and 77777.

How to find the GCF of 77760 and 77777?

We will first find the prime factorization of 77760 and 77777. After we will calculate the factors of 77760 and 77777 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 77777

Prime factors of 77777 are 7, 41, 271. Prime factorization of 77777 in exponential form is:

77777 = 7¹ × 41¹ × 271¹

Step-3: Factors of 77760

List of positive integer factors of 77760 that divides 77760 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

Step-4: Factors of 77777

List of positive integer factors of 77777 that divides 77760 without a remainder.

1, 7, 41, 271, 287, 1897, 11111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77760 and 77777. The biggest common factor number is the GCF number.
So the greatest common factor 77760 and 77777 is 1.

Also check out the Least Common Multiple of 77760 and 77777