What are the divisors of 4493?

1, 4493

There is a total of 2 positive divisors.
The sum of these divisors is 4494.
The arithmetic mean is 2247.

2 odd divisors

1, 4493

How to compute the divisors of 4493?

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 4493 by each of the numbers from 1 to 4493 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)

4493 / 1 = 4493 (the remainder is 0, so 1 is a divisor of 4493)
4493 / 2 = 2246.5 (the remainder is 1, so 2 is not a divisor of 4493)
4493 / 3 = 1497.6666666667 (the remainder is 2, so 3 is not a divisor of 4493)
...
4493 / 4492 = 1.0002226179875 (the remainder is 1, so 4492 is not a divisor of 4493)
4493 / 4493 = 1 (the remainder is 0, so 4493 is a divisor of 4493)

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 4493 (i.e. 67.029844099476). 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 $\frac{N}{d} = D$ )

4493 / 1 = 4493 (the remainder is 0, so 1 and 4493 are divisors of 4493)
4493 / 2 = 2246.5 (the remainder is 1, so 2 is not a divisor of 4493)
4493 / 3 = 1497.6666666667 (the remainder is 2, so 3 is not a divisor of 4493)
...
4493 / 66 = 68.075757575758 (the remainder is 5, so 66 is not a divisor of 4493)
4493 / 67 = 67.059701492537 (the remainder is 4, so 67 is not a divisor of 4493)