What are the divisors of 4491?

1, 3, 9, 499, 1497, 4491

There is a total of 6 positive divisors.
The sum of these divisors is 6500.
The arithmetic mean is 1083.3333333333.

6 odd divisors

1, 3, 9, 499, 1497, 4491

How to compute the divisors of 4491?

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 4491 by each of the numbers from 1 to 4491 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)

4491 / 1 = 4491 (the remainder is 0, so 1 is a divisor of 4491)
4491 / 2 = 2245.5 (the remainder is 1, so 2 is not a divisor of 4491)
4491 / 3 = 1497 (the remainder is 0, so 3 is a divisor of 4491)
...
4491 / 4490 = 1.0002227171492 (the remainder is 1, so 4490 is not a divisor of 4491)
4491 / 4491 = 1 (the remainder is 0, so 4491 is a divisor of 4491)

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 4491 (i.e. 67.014923711066). 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 $\frac{N}{d} = D$ )

4491 / 1 = 4491 (the remainder is 0, so 1 and 4491 are divisors of 4491)
4491 / 2 = 2245.5 (the remainder is 1, so 2 is not a divisor of 4491)
4491 / 3 = 1497 (the remainder is 0, so 3 and 1497 are divisors of 4491)
...
4491 / 66 = 68.045454545455 (the remainder is 3, so 66 is not a divisor of 4491)
4491 / 67 = 67.029850746269 (the remainder is 2, so 67 is not a divisor of 4491)