What are the divisors of 4618?

1, 2, 2309, 4618

There is a total of 4 positive divisors.
The sum of these divisors is 6930.
The arithmetic mean is 1732.5.

2 even divisors

2, 4618

2 odd divisors

1, 2309

How to compute the divisors of 4618?

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 4618 by each of the numbers from 1 to 4618 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)

4618 / 1 = 4618 (the remainder is 0, so 1 is a divisor of 4618)
4618 / 2 = 2309 (the remainder is 0, so 2 is a divisor of 4618)
4618 / 3 = 1539.3333333333 (the remainder is 1, so 3 is not a divisor of 4618)
...
4618 / 4617 = 1.0002165908599 (the remainder is 1, so 4617 is not a divisor of 4618)
4618 / 4618 = 1 (the remainder is 0, so 4618 is a divisor of 4618)

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 4618 (i.e. 67.955868032128). 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 $\frac{N}{d} = D$ )

4618 / 1 = 4618 (the remainder is 0, so 1 and 4618 are divisors of 4618)
4618 / 2 = 2309 (the remainder is 0, so 2 and 2309 are divisors of 4618)
4618 / 3 = 1539.3333333333 (the remainder is 1, so 3 is not a divisor of 4618)
...
4618 / 66 = 69.969696969697 (the remainder is 64, so 66 is not a divisor of 4618)
4618 / 67 = 68.925373134328 (the remainder is 62, so 67 is not a divisor of 4618)