What are the divisors of 1098?

1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, 1098

There is a total of 12 positive divisors.
The sum of these divisors is 2418.
The arithmetic mean is 201.5.

6 even divisors

2, 6, 18, 122, 366, 1098

6 odd divisors

1, 3, 9, 61, 183, 549

How to compute the divisors of 1098?

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 1098 by each of the numbers from 1 to 1098 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)

1098 / 1 = 1098 (the remainder is 0, so 1 is a divisor of 1098)
1098 / 2 = 549 (the remainder is 0, so 2 is a divisor of 1098)
1098 / 3 = 366 (the remainder is 0, so 3 is a divisor of 1098)
...
1098 / 1097 = 1.0009115770283 (the remainder is 1, so 1097 is not a divisor of 1098)
1098 / 1098 = 1 (the remainder is 0, so 1098 is a divisor of 1098)

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 1098 (i.e. 33.136083051562). 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 $\frac{N}{d} = D$ )

1098 / 1 = 1098 (the remainder is 0, so 1 and 1098 are divisors of 1098)
1098 / 2 = 549 (the remainder is 0, so 2 and 549 are divisors of 1098)
1098 / 3 = 366 (the remainder is 0, so 3 and 366 are divisors of 1098)
...
1098 / 32 = 34.3125 (the remainder is 10, so 32 is not a divisor of 1098)
1098 / 33 = 33.272727272727 (the remainder is 9, so 33 is not a divisor of 1098)