What are the divisors of 985?

1, 5, 197, 985

There is a total of 4 positive divisors.
The sum of these divisors is 1188.
The arithmetic mean is 297.

4 odd divisors

1, 5, 197, 985

How to compute the divisors of 985?

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 985 by each of the numbers from 1 to 985 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)

985 / 1 = 985 (the remainder is 0, so 1 is a divisor of 985)
985 / 2 = 492.5 (the remainder is 1, so 2 is not a divisor of 985)
985 / 3 = 328.33333333333 (the remainder is 1, so 3 is not a divisor of 985)
...
985 / 984 = 1.0010162601626 (the remainder is 1, so 984 is not a divisor of 985)
985 / 985 = 1 (the remainder is 0, so 985 is a divisor of 985)

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 985 (i.e. 31.38470965295). 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 $\frac{N}{d} = D$ )

985 / 1 = 985 (the remainder is 0, so 1 and 985 are divisors of 985)
985 / 2 = 492.5 (the remainder is 1, so 2 is not a divisor of 985)
985 / 3 = 328.33333333333 (the remainder is 1, so 3 is not a divisor of 985)
...
985 / 30 = 32.833333333333 (the remainder is 25, so 30 is not a divisor of 985)
985 / 31 = 31.774193548387 (the remainder is 24, so 31 is not a divisor of 985)