What are the divisors of 5446?

1, 2, 7, 14, 389, 778, 2723, 5446

There is a total of 8 positive divisors.
The sum of these divisors is 9360.
The arithmetic mean is 1170.

4 even divisors

2, 14, 778, 5446

4 odd divisors

1, 7, 389, 2723

How to compute the divisors of 5446?

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 5446 by each of the numbers from 1 to 5446 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)

5446 / 1 = 5446 (the remainder is 0, so 1 is a divisor of 5446)
5446 / 2 = 2723 (the remainder is 0, so 2 is a divisor of 5446)
5446 / 3 = 1815.3333333333 (the remainder is 1, so 3 is not a divisor of 5446)
...
5446 / 5445 = 1.0001836547291 (the remainder is 1, so 5445 is not a divisor of 5446)
5446 / 5446 = 1 (the remainder is 0, so 5446 is a divisor of 5446)

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 5446 (i.e. 73.79701890998). 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 $\frac{N}{d} = D$ )

5446 / 1 = 5446 (the remainder is 0, so 1 and 5446 are divisors of 5446)
5446 / 2 = 2723 (the remainder is 0, so 2 and 2723 are divisors of 5446)
5446 / 3 = 1815.3333333333 (the remainder is 1, so 3 is not a divisor of 5446)
...
5446 / 72 = 75.638888888889 (the remainder is 46, so 72 is not a divisor of 5446)
5446 / 73 = 74.602739726027 (the remainder is 44, so 73 is not a divisor of 5446)