What are the divisors of 2098?

1, 2, 1049, 2098

There is a total of 4 positive divisors.
The sum of these divisors is 3150.
The arithmetic mean is 787.5.

2 even divisors

2, 2098

2 odd divisors

1, 1049

How to compute the divisors of 2098?

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 2098 by each of the numbers from 1 to 2098 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)

2098 / 1 = 2098 (the remainder is 0, so 1 is a divisor of 2098)
2098 / 2 = 1049 (the remainder is 0, so 2 is a divisor of 2098)
2098 / 3 = 699.33333333333 (the remainder is 1, so 3 is not a divisor of 2098)
...
2098 / 2097 = 1.0004768717215 (the remainder is 1, so 2097 is not a divisor of 2098)
2098 / 2098 = 1 (the remainder is 0, so 2098 is a divisor of 2098)

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 2098 (i.e. 45.803929962395). 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 $\frac{N}{d} = D$ )

2098 / 1 = 2098 (the remainder is 0, so 1 and 2098 are divisors of 2098)
2098 / 2 = 1049 (the remainder is 0, so 2 and 1049 are divisors of 2098)
2098 / 3 = 699.33333333333 (the remainder is 1, so 3 is not a divisor of 2098)
...
2098 / 44 = 47.681818181818 (the remainder is 30, so 44 is not a divisor of 2098)
2098 / 45 = 46.622222222222 (the remainder is 28, so 45 is not a divisor of 2098)