What are the divisors of 5740?

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 41, 70, 82, 140, 164, 205, 287, 410, 574, 820, 1148, 1435, 2870, 5740

There is a total of 24 positive divisors.
The sum of these divisors is 14112.
The arithmetic mean is 588.

16 even divisors

2, 4, 10, 14, 20, 28, 70, 82, 140, 164, 410, 574, 820, 1148, 2870, 5740

8 odd divisors

1, 5, 7, 35, 41, 205, 287, 1435

How to compute the divisors of 5740?

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 5740 by each of the numbers from 1 to 5740 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)

5740 / 1 = 5740 (the remainder is 0, so 1 is a divisor of 5740)
5740 / 2 = 2870 (the remainder is 0, so 2 is a divisor of 5740)
5740 / 3 = 1913.3333333333 (the remainder is 1, so 3 is not a divisor of 5740)
...
5740 / 5739 = 1.0001742463844 (the remainder is 1, so 5739 is not a divisor of 5740)
5740 / 5740 = 1 (the remainder is 0, so 5740 is a divisor of 5740)

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 5740 (i.e. 75.762787699503). 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 $\frac{N}{d} = D$ )

5740 / 1 = 5740 (the remainder is 0, so 1 and 5740 are divisors of 5740)
5740 / 2 = 2870 (the remainder is 0, so 2 and 2870 are divisors of 5740)
5740 / 3 = 1913.3333333333 (the remainder is 1, so 3 is not a divisor of 5740)
...
5740 / 74 = 77.567567567568 (the remainder is 42, so 74 is not a divisor of 5740)
5740 / 75 = 76.533333333333 (the remainder is 40, so 75 is not a divisor of 5740)