What are the divisors of 5373?

1, 3, 9, 27, 199, 597, 1791, 5373

There is a total of 8 positive divisors.
The sum of these divisors is 8000.
The arithmetic mean is 1000.

8 odd divisors

1, 3, 9, 27, 199, 597, 1791, 5373

How to compute the divisors of 5373?

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 5373 by each of the numbers from 1 to 5373 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)

5373 / 1 = 5373 (the remainder is 0, so 1 is a divisor of 5373)
5373 / 2 = 2686.5 (the remainder is 1, so 2 is not a divisor of 5373)
5373 / 3 = 1791 (the remainder is 0, so 3 is a divisor of 5373)
...
5373 / 5372 = 1.0001861504095 (the remainder is 1, so 5372 is not a divisor of 5373)
5373 / 5373 = 1 (the remainder is 0, so 5373 is a divisor of 5373)

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 5373 (i.e. 73.300750337224). 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 $\frac{N}{d} = D$ )

5373 / 1 = 5373 (the remainder is 0, so 1 and 5373 are divisors of 5373)
5373 / 2 = 2686.5 (the remainder is 1, so 2 is not a divisor of 5373)
5373 / 3 = 1791 (the remainder is 0, so 3 and 1791 are divisors of 5373)
...
5373 / 72 = 74.625 (the remainder is 45, so 72 is not a divisor of 5373)
5373 / 73 = 73.602739726027 (the remainder is 44, so 73 is not a divisor of 5373)