What are the divisors of 4489?

1, 67, 4489

There is a total of 3 positive divisors.
The sum of these divisors is 4557.
The arithmetic mean is 1519.

3 odd divisors

1, 67, 4489

How to compute the divisors of 4489?

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 4489 by each of the numbers from 1 to 4489 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)

4489 / 1 = 4489 (the remainder is 0, so 1 is a divisor of 4489)
4489 / 2 = 2244.5 (the remainder is 1, so 2 is not a divisor of 4489)
4489 / 3 = 1496.3333333333 (the remainder is 1, so 3 is not a divisor of 4489)
...
4489 / 4488 = 1.0002228163993 (the remainder is 1, so 4488 is not a divisor of 4489)
4489 / 4489 = 1 (the remainder is 0, so 4489 is a divisor of 4489)

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 4489 (i.e. 67). 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 $\frac{N}{d} = D$ )

4489 / 1 = 4489 (the remainder is 0, so 1 and 4489 are divisors of 4489)
4489 / 2 = 2244.5 (the remainder is 1, so 2 is not a divisor of 4489)
4489 / 3 = 1496.3333333333 (the remainder is 1, so 3 is not a divisor of 4489)
...
4489 / 66 = 68.015151515152 (the remainder is 1, so 66 is not a divisor of 4489)
4489 / 67 = 67 (the remainder is 0, so 67 and 67 are divisors of 4489)