What are the divisors of 4499?

1, 11, 409, 4499

There is a total of 4 positive divisors.
The sum of these divisors is 4920.
The arithmetic mean is 1230.

4 odd divisors

1, 11, 409, 4499

How to compute the divisors of 4499?

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 4499 by each of the numbers from 1 to 4499 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)

4499 / 1 = 4499 (the remainder is 0, so 1 is a divisor of 4499)
4499 / 2 = 2249.5 (the remainder is 1, so 2 is not a divisor of 4499)
4499 / 3 = 1499.6666666667 (the remainder is 2, so 3 is not a divisor of 4499)
...
4499 / 4498 = 1.0002223210316 (the remainder is 1, so 4498 is not a divisor of 4499)
4499 / 4499 = 1 (the remainder is 0, so 4499 is a divisor of 4499)

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 4499 (i.e. 67.074585350936). 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 $\frac{N}{d} = D$ )

4499 / 1 = 4499 (the remainder is 0, so 1 and 4499 are divisors of 4499)
4499 / 2 = 2249.5 (the remainder is 1, so 2 is not a divisor of 4499)
4499 / 3 = 1499.6666666667 (the remainder is 2, so 3 is not a divisor of 4499)
...
4499 / 66 = 68.166666666667 (the remainder is 11, so 66 is not a divisor of 4499)
4499 / 67 = 67.149253731343 (the remainder is 10, so 67 is not a divisor of 4499)