What are the divisors of 986?

1, 2, 17, 29, 34, 58, 493, 986

There is a total of 8 positive divisors.
The sum of these divisors is 1620.
The arithmetic mean is 202.5.

4 even divisors

2, 34, 58, 986

4 odd divisors

1, 17, 29, 493

How to compute the divisors of 986?

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 986 by each of the numbers from 1 to 986 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)

986 / 1 = 986 (the remainder is 0, so 1 is a divisor of 986)
986 / 2 = 493 (the remainder is 0, so 2 is a divisor of 986)
986 / 3 = 328.66666666667 (the remainder is 2, so 3 is not a divisor of 986)
...
986 / 985 = 1.0010152284264 (the remainder is 1, so 985 is not a divisor of 986)
986 / 986 = 1 (the remainder is 0, so 986 is a divisor of 986)

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 986 (i.e. 31.400636936215). 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 $\frac{N}{d} = D$ )

986 / 1 = 986 (the remainder is 0, so 1 and 986 are divisors of 986)
986 / 2 = 493 (the remainder is 0, so 2 and 493 are divisors of 986)
986 / 3 = 328.66666666667 (the remainder is 2, so 3 is not a divisor of 986)
...
986 / 30 = 32.866666666667 (the remainder is 26, so 30 is not a divisor of 986)
986 / 31 = 31.806451612903 (the remainder is 25, so 31 is not a divisor of 986)