What is the Greatest Common Factor of 77754 and 77760?

Greatest common factor (GCF) of 77754 and 77760 is 6.

GCF(77754,77760) = 6

We will now calculate the prime factors of 77754 and 77760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77754 and 77760.

How to find the GCF of 77754 and 77760?

We will first find the prime factorization of 77754 and 77760. After we will calculate the factors of 77754 and 77760 and find the biggest common factor number .

Step-1: Prime Factorization of 77754

Prime factors of 77754 are 2, 3, 12959. Prime factorization of 77754 in exponential form is:

77754 = 2¹ × 3¹ × 12959¹

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 77754

List of positive integer factors of 77754 that divides 77754 without a remainder.

1, 2, 3, 6, 12959, 25918, 38877

Step-4: Factors of 77760

List of positive integer factors of 77760 that divides 77754 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 77754 and 77760. The biggest common factor number is the GCF number.
So the greatest common factor 77754 and 77760 is 6.

Also check out the Least Common Multiple of 77754 and 77760