What is the Greatest Common Factor of 77760 and 77765?

Greatest common factor (GCF) of 77760 and 77765 is 5.

GCF(77760,77765) = 5

We will now calculate the prime factors of 77760 and 77765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77760 and 77765.

How to find the GCF of 77760 and 77765?

We will first find the prime factorization of 77760 and 77765. After we will calculate the factors of 77760 and 77765 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 77765

Prime factors of 77765 are 5, 103, 151. Prime factorization of 77765 in exponential form is:

77765 = 5¹ × 103¹ × 151¹

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 77765

List of positive integer factors of 77765 that divides 77760 without a remainder.

1, 5, 103, 151, 515, 755, 15553

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77760 and 77765. The biggest common factor number is the GCF number.
So the greatest common factor 77760 and 77765 is 5.

Also check out the Least Common Multiple of 77760 and 77765