What is the Greatest Common Factor of 77588 and 77600?

Greatest common factor (GCF) of 77588 and 77600 is 4.

GCF(77588,77600) = 4

We will now calculate the prime factors of 77588 and 77600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77588 and 77600.

How to find the GCF of 77588 and 77600?

We will first find the prime factorization of 77588 and 77600. After we will calculate the factors of 77588 and 77600 and find the biggest common factor number .

Step-1: Prime Factorization of 77588

Prime factors of 77588 are 2, 7, 17, 163. Prime factorization of 77588 in exponential form is:

77588 = 2² × 7¹ × 17¹ × 163¹

Step-2: Prime Factorization of 77600

Prime factors of 77600 are 2, 5, 97. Prime factorization of 77600 in exponential form is:

77600 = 2⁵ × 5² × 97¹

Step-3: Factors of 77588

List of positive integer factors of 77588 that divides 77588 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 163, 238, 326, 476, 652, 1141, 2282, 2771, 4564, 5542, 11084, 19397, 38794

Step-4: Factors of 77600

List of positive integer factors of 77600 that divides 77588 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 97, 100, 160, 194, 200, 388, 400, 485, 776, 800, 970, 1552, 1940, 2425, 3104, 3880, 4850, 7760, 9700, 15520, 19400, 38800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77588 and 77600. The biggest common factor number is the GCF number.
So the greatest common factor 77588 and 77600 is 4.

Also check out the Least Common Multiple of 77588 and 77600