What are the divisors of 5497?

1, 23, 239, 5497

There is a total of 4 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 1440.

4 odd divisors

1, 23, 239, 5497

How to compute the divisors of 5497?

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 5497 by each of the numbers from 1 to 5497 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)

5497 / 1 = 5497 (the remainder is 0, so 1 is a divisor of 5497)
5497 / 2 = 2748.5 (the remainder is 1, so 2 is not a divisor of 5497)
5497 / 3 = 1832.3333333333 (the remainder is 1, so 3 is not a divisor of 5497)
...
5497 / 5496 = 1.0001819505095 (the remainder is 1, so 5496 is not a divisor of 5497)
5497 / 5497 = 1 (the remainder is 0, so 5497 is a divisor of 5497)

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 5497 (i.e. 74.14175611624). 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 $\frac{N}{d} = D$ )

5497 / 1 = 5497 (the remainder is 0, so 1 and 5497 are divisors of 5497)
5497 / 2 = 2748.5 (the remainder is 1, so 2 is not a divisor of 5497)
5497 / 3 = 1832.3333333333 (the remainder is 1, so 3 is not a divisor of 5497)
...
5497 / 73 = 75.301369863014 (the remainder is 22, so 73 is not a divisor of 5497)
5497 / 74 = 74.283783783784 (the remainder is 21, so 74 is not a divisor of 5497)