What are the divisors of 5435?

1, 5, 1087, 5435

There is a total of 4 positive divisors.
The sum of these divisors is 6528.
The arithmetic mean is 1632.

4 odd divisors

1, 5, 1087, 5435

How to compute the divisors of 5435?

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 5435 by each of the numbers from 1 to 5435 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)

5435 / 1 = 5435 (the remainder is 0, so 1 is a divisor of 5435)
5435 / 2 = 2717.5 (the remainder is 1, so 2 is not a divisor of 5435)
5435 / 3 = 1811.6666666667 (the remainder is 2, so 3 is not a divisor of 5435)
...
5435 / 5434 = 1.0001840264998 (the remainder is 1, so 5434 is not a divisor of 5435)
5435 / 5435 = 1 (the remainder is 0, so 5435 is a divisor of 5435)

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 5435 (i.e. 73.722452482266). 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 $\frac{N}{d} = D$ )

5435 / 1 = 5435 (the remainder is 0, so 1 and 5435 are divisors of 5435)
5435 / 2 = 2717.5 (the remainder is 1, so 2 is not a divisor of 5435)
5435 / 3 = 1811.6666666667 (the remainder is 2, so 3 is not a divisor of 5435)
...
5435 / 72 = 75.486111111111 (the remainder is 35, so 72 is not a divisor of 5435)
5435 / 73 = 74.452054794521 (the remainder is 33, so 73 is not a divisor of 5435)