What are the divisors of 982?

1, 2, 491, 982

There is a total of 4 positive divisors.
The sum of these divisors is 1476.
The arithmetic mean is 369.

2 even divisors

2, 982

2 odd divisors

1, 491

How to compute the divisors of 982?

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 982 by each of the numbers from 1 to 982 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)

982 / 1 = 982 (the remainder is 0, so 1 is a divisor of 982)
982 / 2 = 491 (the remainder is 0, so 2 is a divisor of 982)
982 / 3 = 327.33333333333 (the remainder is 1, so 3 is not a divisor of 982)
...
982 / 981 = 1.0010193679918 (the remainder is 1, so 981 is not a divisor of 982)
982 / 982 = 1 (the remainder is 0, so 982 is a divisor of 982)

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 982 (i.e. 31.336879231985). 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 $\frac{N}{d} = D$ )

982 / 1 = 982 (the remainder is 0, so 1 and 982 are divisors of 982)
982 / 2 = 491 (the remainder is 0, so 2 and 491 are divisors of 982)
982 / 3 = 327.33333333333 (the remainder is 1, so 3 is not a divisor of 982)
...
982 / 30 = 32.733333333333 (the remainder is 22, so 30 is not a divisor of 982)
982 / 31 = 31.677419354839 (the remainder is 21, so 31 is not a divisor of 982)