What are the divisors of 5410?

1, 2, 5, 10, 541, 1082, 2705, 5410

There is a total of 8 positive divisors.
The sum of these divisors is 9756.
The arithmetic mean is 1219.5.

4 even divisors

2, 10, 1082, 5410

4 odd divisors

1, 5, 541, 2705

How to compute the divisors of 5410?

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 5410 by each of the numbers from 1 to 5410 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)

5410 / 1 = 5410 (the remainder is 0, so 1 is a divisor of 5410)
5410 / 2 = 2705 (the remainder is 0, so 2 is a divisor of 5410)
5410 / 3 = 1803.3333333333 (the remainder is 1, so 3 is not a divisor of 5410)
...
5410 / 5409 = 1.0001848770568 (the remainder is 1, so 5409 is not a divisor of 5410)
5410 / 5410 = 1 (the remainder is 0, so 5410 is a divisor of 5410)

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 5410 (i.e. 73.552702193733). 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 $\frac{N}{d} = D$ )

5410 / 1 = 5410 (the remainder is 0, so 1 and 5410 are divisors of 5410)
5410 / 2 = 2705 (the remainder is 0, so 2 and 2705 are divisors of 5410)
5410 / 3 = 1803.3333333333 (the remainder is 1, so 3 is not a divisor of 5410)
...
5410 / 72 = 75.138888888889 (the remainder is 10, so 72 is not a divisor of 5410)
5410 / 73 = 74.109589041096 (the remainder is 8, so 73 is not a divisor of 5410)