What are the divisors of 998?

1, 2, 499, 998

There is a total of 4 positive divisors.
The sum of these divisors is 1500.
The arithmetic mean is 375.

2 even divisors

2, 998

2 odd divisors

1, 499

How to compute the divisors of 998?

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 998 by each of the numbers from 1 to 998 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)

998 / 1 = 998 (the remainder is 0, so 1 is a divisor of 998)
998 / 2 = 499 (the remainder is 0, so 2 is a divisor of 998)
998 / 3 = 332.66666666667 (the remainder is 2, so 3 is not a divisor of 998)
...
998 / 997 = 1.0010030090271 (the remainder is 1, so 997 is not a divisor of 998)
998 / 998 = 1 (the remainder is 0, so 998 is a divisor of 998)

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 998 (i.e. 31.591137997863). 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 $\frac{N}{d} = D$ )

998 / 1 = 998 (the remainder is 0, so 1 and 998 are divisors of 998)
998 / 2 = 499 (the remainder is 0, so 2 and 499 are divisors of 998)
998 / 3 = 332.66666666667 (the remainder is 2, so 3 is not a divisor of 998)
...
998 / 30 = 33.266666666667 (the remainder is 8, so 30 is not a divisor of 998)
998 / 31 = 32.193548387097 (the remainder is 6, so 31 is not a divisor of 998)