What are the divisors of 2198?

1, 2, 7, 14, 157, 314, 1099, 2198

There is a total of 8 positive divisors.
The sum of these divisors is 3792.
The arithmetic mean is 474.

4 even divisors

2, 14, 314, 2198

4 odd divisors

1, 7, 157, 1099

How to compute the divisors of 2198?

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 2198 by each of the numbers from 1 to 2198 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)

2198 / 1 = 2198 (the remainder is 0, so 1 is a divisor of 2198)
2198 / 2 = 1099 (the remainder is 0, so 2 is a divisor of 2198)
2198 / 3 = 732.66666666667 (the remainder is 2, so 3 is not a divisor of 2198)
...
2198 / 2197 = 1.0004551661356 (the remainder is 1, so 2197 is not a divisor of 2198)
2198 / 2198 = 1 (the remainder is 0, so 2198 is a divisor of 2198)

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 2198 (i.e. 46.882832678924). 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 $\frac{N}{d} = D$ )

2198 / 1 = 2198 (the remainder is 0, so 1 and 2198 are divisors of 2198)
2198 / 2 = 1099 (the remainder is 0, so 2 and 1099 are divisors of 2198)
2198 / 3 = 732.66666666667 (the remainder is 2, so 3 is not a divisor of 2198)
...
2198 / 45 = 48.844444444444 (the remainder is 38, so 45 is not a divisor of 2198)
2198 / 46 = 47.782608695652 (the remainder is 36, so 46 is not a divisor of 2198)