What are the divisors of 987?

1, 3, 7, 21, 47, 141, 329, 987

There is a total of 8 positive divisors.
The sum of these divisors is 1536.
The arithmetic mean is 192.

8 odd divisors

1, 3, 7, 21, 47, 141, 329, 987

How to compute the divisors of 987?

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 987 by each of the numbers from 1 to 987 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)

987 / 1 = 987 (the remainder is 0, so 1 is a divisor of 987)
987 / 2 = 493.5 (the remainder is 1, so 2 is not a divisor of 987)
987 / 3 = 329 (the remainder is 0, so 3 is a divisor of 987)
...
987 / 986 = 1.001014198783 (the remainder is 1, so 986 is not a divisor of 987)
987 / 987 = 1 (the remainder is 0, so 987 is a divisor of 987)

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 987 (i.e. 31.41655614481). 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 $\frac{N}{d} = D$ )

987 / 1 = 987 (the remainder is 0, so 1 and 987 are divisors of 987)
987 / 2 = 493.5 (the remainder is 1, so 2 is not a divisor of 987)
987 / 3 = 329 (the remainder is 0, so 3 and 329 are divisors of 987)
...
987 / 30 = 32.9 (the remainder is 27, so 30 is not a divisor of 987)
987 / 31 = 31.838709677419 (the remainder is 26, so 31 is not a divisor of 987)