What are the divisors of 4098?

1, 2, 3, 6, 683, 1366, 2049, 4098

There is a total of 8 positive divisors.
The sum of these divisors is 8208.
The arithmetic mean is 1026.

4 even divisors

2, 6, 1366, 4098

4 odd divisors

1, 3, 683, 2049

How to compute the divisors of 4098?

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 4098 by each of the numbers from 1 to 4098 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)

4098 / 1 = 4098 (the remainder is 0, so 1 is a divisor of 4098)
4098 / 2 = 2049 (the remainder is 0, so 2 is a divisor of 4098)
4098 / 3 = 1366 (the remainder is 0, so 3 is a divisor of 4098)
...
4098 / 4097 = 1.0002440810349 (the remainder is 1, so 4097 is not a divisor of 4098)
4098 / 4098 = 1 (the remainder is 0, so 4098 is a divisor of 4098)

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 4098 (i.e. 64.015623093117). 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 $\frac{N}{d} = D$ )

4098 / 1 = 4098 (the remainder is 0, so 1 and 4098 are divisors of 4098)
4098 / 2 = 2049 (the remainder is 0, so 2 and 2049 are divisors of 4098)
4098 / 3 = 1366 (the remainder is 0, so 3 and 1366 are divisors of 4098)
...
4098 / 63 = 65.047619047619 (the remainder is 3, so 63 is not a divisor of 4098)
4098 / 64 = 64.03125 (the remainder is 2, so 64 is not a divisor of 4098)