What are the divisors of 4609?

1, 11, 419, 4609

There is a total of 4 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 1260.

4 odd divisors

1, 11, 419, 4609

How to compute the divisors of 4609?

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 4609 by each of the numbers from 1 to 4609 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)

4609 / 1 = 4609 (the remainder is 0, so 1 is a divisor of 4609)
4609 / 2 = 2304.5 (the remainder is 1, so 2 is not a divisor of 4609)
4609 / 3 = 1536.3333333333 (the remainder is 1, so 3 is not a divisor of 4609)
...
4609 / 4608 = 1.0002170138889 (the remainder is 1, so 4608 is not a divisor of 4609)
4609 / 4609 = 1 (the remainder is 0, so 4609 is a divisor of 4609)

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 4609 (i.e. 67.889616289975). 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 $\frac{N}{d} = D$ )

4609 / 1 = 4609 (the remainder is 0, so 1 and 4609 are divisors of 4609)
4609 / 2 = 2304.5 (the remainder is 1, so 2 is not a divisor of 4609)
4609 / 3 = 1536.3333333333 (the remainder is 1, so 3 is not a divisor of 4609)
...
4609 / 66 = 69.833333333333 (the remainder is 55, so 66 is not a divisor of 4609)
4609 / 67 = 68.791044776119 (the remainder is 53, so 67 is not a divisor of 4609)