What are the divisors of 983?

1, 983

There is a total of 2 positive divisors.
The sum of these divisors is 984.
The arithmetic mean is 492.

2 odd divisors

1, 983

How to compute the divisors of 983?

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 983 by each of the numbers from 1 to 983 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)

983 / 1 = 983 (the remainder is 0, so 1 is a divisor of 983)
983 / 2 = 491.5 (the remainder is 1, so 2 is not a divisor of 983)
983 / 3 = 327.66666666667 (the remainder is 2, so 3 is not a divisor of 983)
...
983 / 982 = 1.0010183299389 (the remainder is 1, so 982 is not a divisor of 983)
983 / 983 = 1 (the remainder is 0, so 983 is a divisor of 983)

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 983 (i.e. 31.352830813182). 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 $\frac{N}{d} = D$ )

983 / 1 = 983 (the remainder is 0, so 1 and 983 are divisors of 983)
983 / 2 = 491.5 (the remainder is 1, so 2 is not a divisor of 983)
983 / 3 = 327.66666666667 (the remainder is 2, so 3 is not a divisor of 983)
...
983 / 30 = 32.766666666667 (the remainder is 23, so 30 is not a divisor of 983)
983 / 31 = 31.709677419355 (the remainder is 22, so 31 is not a divisor of 983)