What are the divisors of 1487?

1, 1487

There is a total of 2 positive divisors.
The sum of these divisors is 1488.
The arithmetic mean is 744.

2 odd divisors

1, 1487

How to compute the divisors of 1487?

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 1487 by each of the numbers from 1 to 1487 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)

1487 / 1 = 1487 (the remainder is 0, so 1 is a divisor of 1487)
1487 / 2 = 743.5 (the remainder is 1, so 2 is not a divisor of 1487)
1487 / 3 = 495.66666666667 (the remainder is 2, so 3 is not a divisor of 1487)
...
1487 / 1486 = 1.0006729475101 (the remainder is 1, so 1486 is not a divisor of 1487)
1487 / 1487 = 1 (the remainder is 0, so 1487 is a divisor of 1487)

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 1487 (i.e. 38.561638969318). 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 $\frac{N}{d} = D$ )

1487 / 1 = 1487 (the remainder is 0, so 1 and 1487 are divisors of 1487)
1487 / 2 = 743.5 (the remainder is 1, so 2 is not a divisor of 1487)
1487 / 3 = 495.66666666667 (the remainder is 2, so 3 is not a divisor of 1487)
...
1487 / 37 = 40.189189189189 (the remainder is 7, so 37 is not a divisor of 1487)
1487 / 38 = 39.131578947368 (the remainder is 5, so 38 is not a divisor of 1487)