What are the divisors of 1982?

1, 2, 991, 1982

There is a total of 4 positive divisors.
The sum of these divisors is 2976.
The arithmetic mean is 744.

2 even divisors

2, 1982

2 odd divisors

1, 991

How to compute the divisors of 1982?

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 1982 by each of the numbers from 1 to 1982 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)

1982 / 1 = 1982 (the remainder is 0, so 1 is a divisor of 1982)
1982 / 2 = 991 (the remainder is 0, so 2 is a divisor of 1982)
1982 / 3 = 660.66666666667 (the remainder is 2, so 3 is not a divisor of 1982)
...
1982 / 1981 = 1.0005047955578 (the remainder is 1, so 1981 is not a divisor of 1982)
1982 / 1982 = 1 (the remainder is 0, so 1982 is a divisor of 1982)

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 1982 (i.e. 44.519658579104). 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 $\frac{N}{d} = D$ )

1982 / 1 = 1982 (the remainder is 0, so 1 and 1982 are divisors of 1982)
1982 / 2 = 991 (the remainder is 0, so 2 and 991 are divisors of 1982)
1982 / 3 = 660.66666666667 (the remainder is 2, so 3 is not a divisor of 1982)
...
1982 / 43 = 46.093023255814 (the remainder is 4, so 43 is not a divisor of 1982)
1982 / 44 = 45.045454545455 (the remainder is 2, so 44 is not a divisor of 1982)