What is the Greatest Common Factor of 76585 and 76600?

Greatest common factor (GCF) of 76585 and 76600 is 5.

GCF(76585,76600) = 5

We will now calculate the prime factors of 76585 and 76600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76585 and 76600.

How to find the GCF of 76585 and 76600?

We will first find the prime factorization of 76585 and 76600. After we will calculate the factors of 76585 and 76600 and find the biggest common factor number .

Step-1: Prime Factorization of 76585

Prime factors of 76585 are 5, 17, 53. Prime factorization of 76585 in exponential form is:

76585 = 5¹ × 17² × 53¹

Step-2: Prime Factorization of 76600

Prime factors of 76600 are 2, 5, 383. Prime factorization of 76600 in exponential form is:

76600 = 2³ × 5² × 383¹

Step-3: Factors of 76585

List of positive integer factors of 76585 that divides 76585 without a remainder.

1, 5, 17, 53, 85, 265, 289, 901, 1445, 4505, 15317

Step-4: Factors of 76600

List of positive integer factors of 76600 that divides 76585 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 383, 766, 1532, 1915, 3064, 3830, 7660, 9575, 15320, 19150, 38300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76585 and 76600. The biggest common factor number is the GCF number.
So the greatest common factor 76585 and 76600 is 5.

Also check out the Least Common Multiple of 76585 and 76600