What is the Greatest Common Factor of 77760 and 77774?

Greatest common factor (GCF) of 77760 and 77774 is 2.

GCF(77760,77774) = 2

We will now calculate the prime factors of 77760 and 77774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77760 and 77774.

How to find the GCF of 77760 and 77774?

We will first find the prime factorization of 77760 and 77774. After we will calculate the factors of 77760 and 77774 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 77774

Prime factors of 77774 are 2, 37, 1051. Prime factorization of 77774 in exponential form is:

77774 = 2¹ × 37¹ × 1051¹

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 77774

List of positive integer factors of 77774 that divides 77760 without a remainder.

1, 2, 37, 74, 1051, 2102, 38887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77760 and 77774. The biggest common factor number is the GCF number.
So the greatest common factor 77760 and 77774 is 2.

Also check out the Least Common Multiple of 77760 and 77774