What are the divisors of 5481?

1, 3, 7, 9, 21, 27, 29, 63, 87, 189, 203, 261, 609, 783, 1827, 5481

There is a total of 16 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 600.

16 odd divisors

1, 3, 7, 9, 21, 27, 29, 63, 87, 189, 203, 261, 609, 783, 1827, 5481

How to compute the divisors of 5481?

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 5481 by each of the numbers from 1 to 5481 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)

5481 / 1 = 5481 (the remainder is 0, so 1 is a divisor of 5481)
5481 / 2 = 2740.5 (the remainder is 1, so 2 is not a divisor of 5481)
5481 / 3 = 1827 (the remainder is 0, so 3 is a divisor of 5481)
...
5481 / 5480 = 1.0001824817518 (the remainder is 1, so 5480 is not a divisor of 5481)
5481 / 5481 = 1 (the remainder is 0, so 5481 is a divisor of 5481)

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 5481 (i.e. 74.033776075518). 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 $\frac{N}{d} = D$ )

5481 / 1 = 5481 (the remainder is 0, so 1 and 5481 are divisors of 5481)
5481 / 2 = 2740.5 (the remainder is 1, so 2 is not a divisor of 5481)
5481 / 3 = 1827 (the remainder is 0, so 3 and 1827 are divisors of 5481)
...
5481 / 73 = 75.082191780822 (the remainder is 6, so 73 is not a divisor of 5481)
5481 / 74 = 74.067567567568 (the remainder is 5, so 74 is not a divisor of 5481)