What are the divisors of 989?

1, 23, 43, 989

There is a total of 4 positive divisors.
The sum of these divisors is 1056.
The arithmetic mean is 264.

4 odd divisors

1, 23, 43, 989

How to compute the divisors of 989?

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 989 by each of the numbers from 1 to 989 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)

989 / 1 = 989 (the remainder is 0, so 1 is a divisor of 989)
989 / 2 = 494.5 (the remainder is 1, so 2 is not a divisor of 989)
989 / 3 = 329.66666666667 (the remainder is 2, so 3 is not a divisor of 989)
...
989 / 988 = 1.001012145749 (the remainder is 1, so 988 is not a divisor of 989)
989 / 989 = 1 (the remainder is 0, so 989 is a divisor of 989)

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 989 (i.e. 31.448370387033). 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 $\frac{N}{d} = D$ )

989 / 1 = 989 (the remainder is 0, so 1 and 989 are divisors of 989)
989 / 2 = 494.5 (the remainder is 1, so 2 is not a divisor of 989)
989 / 3 = 329.66666666667 (the remainder is 2, so 3 is not a divisor of 989)
...
989 / 30 = 32.966666666667 (the remainder is 29, so 30 is not a divisor of 989)
989 / 31 = 31.903225806452 (the remainder is 28, so 31 is not a divisor of 989)