What are the divisors of 1987?

1, 1987

There is a total of 2 positive divisors.
The sum of these divisors is 1988.
The arithmetic mean is 994.

2 odd divisors

1, 1987

How to compute the divisors of 1987?

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 1987 by each of the numbers from 1 to 1987 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)

1987 / 1 = 1987 (the remainder is 0, so 1 is a divisor of 1987)
1987 / 2 = 993.5 (the remainder is 1, so 2 is not a divisor of 1987)
1987 / 3 = 662.33333333333 (the remainder is 1, so 3 is not a divisor of 1987)
...
1987 / 1986 = 1.0005035246727 (the remainder is 1, so 1986 is not a divisor of 1987)
1987 / 1987 = 1 (the remainder is 0, so 1987 is a divisor of 1987)

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 1987 (i.e. 44.575778176045). 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 $\frac{N}{d} = D$ )

1987 / 1 = 1987 (the remainder is 0, so 1 and 1987 are divisors of 1987)
1987 / 2 = 993.5 (the remainder is 1, so 2 is not a divisor of 1987)
1987 / 3 = 662.33333333333 (the remainder is 1, so 3 is not a divisor of 1987)
...
1987 / 43 = 46.209302325581 (the remainder is 9, so 43 is not a divisor of 1987)
1987 / 44 = 45.159090909091 (the remainder is 7, so 44 is not a divisor of 1987)