What are the divisors of 3099?

1, 3, 1033, 3099

There is a total of 4 positive divisors.
The sum of these divisors is 4136.
The arithmetic mean is 1034.

4 odd divisors

1, 3, 1033, 3099

How to compute the divisors of 3099?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3099 by each of the numbers from 1 to 3099 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3099 / 1 = 3099 (the remainder is 0, so 1 is a divisor of 3099)
3099 / 2 = 1549.5 (the remainder is 1, so 2 is not a divisor of 3099)
3099 / 3 = 1033 (the remainder is 0, so 3 is a divisor of 3099)
...
3099 / 3098 = 1.0003227888961 (the remainder is 1, so 3098 is not a divisor of 3099)
3099 / 3099 = 1 (the remainder is 0, so 3099 is a divisor of 3099)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3099 (i.e. 55.668662638867). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3099 / 1 = 3099 (the remainder is 0, so 1 and 3099 are divisors of 3099)
3099 / 2 = 1549.5 (the remainder is 1, so 2 is not a divisor of 3099)
3099 / 3 = 1033 (the remainder is 0, so 3 and 1033 are divisors of 3099)
...
3099 / 54 = 57.388888888889 (the remainder is 21, so 54 is not a divisor of 3099)
3099 / 55 = 56.345454545455 (the remainder is 19, so 55 is not a divisor of 3099)