What are the divisors of 5345?

1, 5, 1069, 5345

There is a total of 4 positive divisors.
The sum of these divisors is 6420.
The arithmetic mean is 1605.

4 odd divisors

1, 5, 1069, 5345

How to compute the divisors of 5345?

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 5345 by each of the numbers from 1 to 5345 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)

5345 / 1 = 5345 (the remainder is 0, so 1 is a divisor of 5345)
5345 / 2 = 2672.5 (the remainder is 1, so 2 is not a divisor of 5345)
5345 / 3 = 1781.6666666667 (the remainder is 2, so 3 is not a divisor of 5345)
...
5345 / 5344 = 1.0001871257485 (the remainder is 1, so 5344 is not a divisor of 5345)
5345 / 5345 = 1 (the remainder is 0, so 5345 is a divisor of 5345)

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 5345 (i.e. 73.109506905737). 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 $\frac{N}{d} = D$ )

5345 / 1 = 5345 (the remainder is 0, so 1 and 5345 are divisors of 5345)
5345 / 2 = 2672.5 (the remainder is 1, so 2 is not a divisor of 5345)
5345 / 3 = 1781.6666666667 (the remainder is 2, so 3 is not a divisor of 5345)
...
5345 / 72 = 74.236111111111 (the remainder is 17, so 72 is not a divisor of 5345)
5345 / 73 = 73.219178082192 (the remainder is 16, so 73 is not a divisor of 5345)