What are the divisors of 5397?

1, 3, 7, 21, 257, 771, 1799, 5397

There is a total of 8 positive divisors.
The sum of these divisors is 8256.
The arithmetic mean is 1032.

8 odd divisors

1, 3, 7, 21, 257, 771, 1799, 5397

How to compute the divisors of 5397?

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 5397 by each of the numbers from 1 to 5397 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)

5397 / 1 = 5397 (the remainder is 0, so 1 is a divisor of 5397)
5397 / 2 = 2698.5 (the remainder is 1, so 2 is not a divisor of 5397)
5397 / 3 = 1799 (the remainder is 0, so 3 is a divisor of 5397)
...
5397 / 5396 = 1.0001853224611 (the remainder is 1, so 5396 is not a divisor of 5397)
5397 / 5397 = 1 (the remainder is 0, so 5397 is a divisor of 5397)

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 5397 (i.e. 73.464277033127). 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 $\frac{N}{d} = D$ )

5397 / 1 = 5397 (the remainder is 0, so 1 and 5397 are divisors of 5397)
5397 / 2 = 2698.5 (the remainder is 1, so 2 is not a divisor of 5397)
5397 / 3 = 1799 (the remainder is 0, so 3 and 1799 are divisors of 5397)
...
5397 / 72 = 74.958333333333 (the remainder is 69, so 72 is not a divisor of 5397)
5397 / 73 = 73.931506849315 (the remainder is 68, so 73 is not a divisor of 5397)