What is the Greatest Common Factor of 77760 and 77780?

Greatest common factor (GCF) of 77760 and 77780 is 20.

GCF(77760,77780) = 20

We will now calculate the prime factors of 77760 and 77780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77760 and 77780.

How to find the GCF of 77760 and 77780?

We will first find the prime factorization of 77760 and 77780. After we will calculate the factors of 77760 and 77780 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 77780

Prime factors of 77780 are 2, 5, 3889. Prime factorization of 77780 in exponential form is:

77780 = 2² × 5¹ × 3889¹

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 77780

List of positive integer factors of 77780 that divides 77760 without a remainder.

1, 2, 4, 5, 10, 20, 3889, 7778, 15556, 19445, 38890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77760 and 77780. The biggest common factor number is the GCF number.
So the greatest common factor 77760 and 77780 is 20.

Also check out the Least Common Multiple of 77760 and 77780