What is the Greatest Common Factor of 16585 and 16600?

Greatest common factor (GCF) of 16585 and 16600 is 5.

GCF(16585,16600) = 5

We will now calculate the prime factors of 16585 and 16600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16585 and 16600.

How to find the GCF of 16585 and 16600?

We will first find the prime factorization of 16585 and 16600. After we will calculate the factors of 16585 and 16600 and find the biggest common factor number .

Step-1: Prime Factorization of 16585

Prime factors of 16585 are 5, 31, 107. Prime factorization of 16585 in exponential form is:

16585 = 5¹ × 31¹ × 107¹

Step-2: Prime Factorization of 16600

Prime factors of 16600 are 2, 5, 83. Prime factorization of 16600 in exponential form is:

16600 = 2³ × 5² × 83¹

Step-3: Factors of 16585

List of positive integer factors of 16585 that divides 16585 without a remainder.

1, 5, 31, 107, 155, 535, 3317

Step-4: Factors of 16600

List of positive integer factors of 16600 that divides 16585 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 83, 100, 166, 200, 332, 415, 664, 830, 1660, 2075, 3320, 4150, 8300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16585 and 16600. The biggest common factor number is the GCF number.
So the greatest common factor 16585 and 16600 is 5.

Also check out the Least Common Multiple of 16585 and 16600