What are the divisors of 5349?

1, 3, 1783, 5349

There is a total of 4 positive divisors.
The sum of these divisors is 7136.
The arithmetic mean is 1784.

4 odd divisors

1, 3, 1783, 5349

How to compute the divisors of 5349?

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 5349 by each of the numbers from 1 to 5349 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)

5349 / 1 = 5349 (the remainder is 0, so 1 is a divisor of 5349)
5349 / 2 = 2674.5 (the remainder is 1, so 2 is not a divisor of 5349)
5349 / 3 = 1783 (the remainder is 0, so 3 is a divisor of 5349)
...
5349 / 5348 = 1.0001869857891 (the remainder is 1, so 5348 is not a divisor of 5349)
5349 / 5349 = 1 (the remainder is 0, so 5349 is a divisor of 5349)

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 5349 (i.e. 73.136858012906). 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 $\frac{N}{d} = D$ )

5349 / 1 = 5349 (the remainder is 0, so 1 and 5349 are divisors of 5349)
5349 / 2 = 2674.5 (the remainder is 1, so 2 is not a divisor of 5349)
5349 / 3 = 1783 (the remainder is 0, so 3 and 1783 are divisors of 5349)
...
5349 / 72 = 74.291666666667 (the remainder is 21, so 72 is not a divisor of 5349)
5349 / 73 = 73.27397260274 (the remainder is 20, so 73 is not a divisor of 5349)