What are the divisors of 4459?

1, 7, 13, 49, 91, 343, 637, 4459

There is a total of 8 positive divisors.
The sum of these divisors is 5600.
The arithmetic mean is 700.

8 odd divisors

1, 7, 13, 49, 91, 343, 637, 4459

How to compute the divisors of 4459?

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 4459 by each of the numbers from 1 to 4459 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)

4459 / 1 = 4459 (the remainder is 0, so 1 is a divisor of 4459)
4459 / 2 = 2229.5 (the remainder is 1, so 2 is not a divisor of 4459)
4459 / 3 = 1486.3333333333 (the remainder is 1, so 3 is not a divisor of 4459)
...
4459 / 4458 = 1.0002243158367 (the remainder is 1, so 4458 is not a divisor of 4459)
4459 / 4459 = 1 (the remainder is 0, so 4459 is a divisor of 4459)

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 4459 (i.e. 66.775744099186). 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 $\frac{N}{d} = D$ )

4459 / 1 = 4459 (the remainder is 0, so 1 and 4459 are divisors of 4459)
4459 / 2 = 2229.5 (the remainder is 1, so 2 is not a divisor of 4459)
4459 / 3 = 1486.3333333333 (the remainder is 1, so 3 is not a divisor of 4459)
...
4459 / 65 = 68.6 (the remainder is 39, so 65 is not a divisor of 4459)
4459 / 66 = 67.560606060606 (the remainder is 37, so 66 is not a divisor of 4459)