What are the divisors of 5426?

1, 2, 2713, 5426

There is a total of 4 positive divisors.
The sum of these divisors is 8142.
The arithmetic mean is 2035.5.

2 even divisors

2, 5426

2 odd divisors

1, 2713

How to compute the divisors of 5426?

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 5426 by each of the numbers from 1 to 5426 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)

5426 / 1 = 5426 (the remainder is 0, so 1 is a divisor of 5426)
5426 / 2 = 2713 (the remainder is 0, so 2 is a divisor of 5426)
5426 / 3 = 1808.6666666667 (the remainder is 2, so 3 is not a divisor of 5426)
...
5426 / 5425 = 1.0001843317972 (the remainder is 1, so 5425 is not a divisor of 5426)
5426 / 5426 = 1 (the remainder is 0, so 5426 is a divisor of 5426)

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 5426 (i.e. 73.661387442812). 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 $\frac{N}{d} = D$ )

5426 / 1 = 5426 (the remainder is 0, so 1 and 5426 are divisors of 5426)
5426 / 2 = 2713 (the remainder is 0, so 2 and 2713 are divisors of 5426)
5426 / 3 = 1808.6666666667 (the remainder is 2, so 3 is not a divisor of 5426)
...
5426 / 72 = 75.361111111111 (the remainder is 26, so 72 is not a divisor of 5426)
5426 / 73 = 74.328767123288 (the remainder is 24, so 73 is not a divisor of 5426)