What are the divisors of 5487?

1, 3, 31, 59, 93, 177, 1829, 5487

There is a total of 8 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 960.

8 odd divisors

1, 3, 31, 59, 93, 177, 1829, 5487

How to compute the divisors of 5487?

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 5487 by each of the numbers from 1 to 5487 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)

5487 / 1 = 5487 (the remainder is 0, so 1 is a divisor of 5487)
5487 / 2 = 2743.5 (the remainder is 1, so 2 is not a divisor of 5487)
5487 / 3 = 1829 (the remainder is 0, so 3 is a divisor of 5487)
...
5487 / 5486 = 1.0001822821728 (the remainder is 1, so 5486 is not a divisor of 5487)
5487 / 5487 = 1 (the remainder is 0, so 5487 is a divisor of 5487)

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 5487 (i.e. 74.074287036731). 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 $\frac{N}{d} = D$ )

5487 / 1 = 5487 (the remainder is 0, so 1 and 5487 are divisors of 5487)
5487 / 2 = 2743.5 (the remainder is 1, so 2 is not a divisor of 5487)
5487 / 3 = 1829 (the remainder is 0, so 3 and 1829 are divisors of 5487)
...
5487 / 73 = 75.164383561644 (the remainder is 12, so 73 is not a divisor of 5487)
5487 / 74 = 74.148648648649 (the remainder is 11, so 74 is not a divisor of 5487)