What are the divisors of 5442?

1, 2, 3, 6, 907, 1814, 2721, 5442

There is a total of 8 positive divisors.
The sum of these divisors is 10896.
The arithmetic mean is 1362.

4 even divisors

2, 6, 1814, 5442

4 odd divisors

1, 3, 907, 2721

How to compute the divisors of 5442?

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 5442 by each of the numbers from 1 to 5442 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)

5442 / 1 = 5442 (the remainder is 0, so 1 is a divisor of 5442)
5442 / 2 = 2721 (the remainder is 0, so 2 is a divisor of 5442)
5442 / 3 = 1814 (the remainder is 0, so 3 is a divisor of 5442)
...
5442 / 5441 = 1.0001837897445 (the remainder is 1, so 5441 is not a divisor of 5442)
5442 / 5442 = 1 (the remainder is 0, so 5442 is a divisor of 5442)

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 5442 (i.e. 73.769912566032). 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 $\frac{N}{d} = D$ )

5442 / 1 = 5442 (the remainder is 0, so 1 and 5442 are divisors of 5442)
5442 / 2 = 2721 (the remainder is 0, so 2 and 2721 are divisors of 5442)
5442 / 3 = 1814 (the remainder is 0, so 3 and 1814 are divisors of 5442)
...
5442 / 72 = 75.583333333333 (the remainder is 42, so 72 is not a divisor of 5442)
5442 / 73 = 74.547945205479 (the remainder is 40, so 73 is not a divisor of 5442)