What are the divisors of 5747?

1, 7, 821, 5747

There is a total of 4 positive divisors.
The sum of these divisors is 6576.
The arithmetic mean is 1644.

4 odd divisors

1, 7, 821, 5747

How to compute the divisors of 5747?

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 5747 by each of the numbers from 1 to 5747 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)

5747 / 1 = 5747 (the remainder is 0, so 1 is a divisor of 5747)
5747 / 2 = 2873.5 (the remainder is 1, so 2 is not a divisor of 5747)
5747 / 3 = 1915.6666666667 (the remainder is 2, so 3 is not a divisor of 5747)
...
5747 / 5746 = 1.0001740341107 (the remainder is 1, so 5746 is not a divisor of 5747)
5747 / 5747 = 1 (the remainder is 0, so 5747 is a divisor of 5747)

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 5747 (i.e. 75.808970445456). 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 $\frac{N}{d} = D$ )

5747 / 1 = 5747 (the remainder is 0, so 1 and 5747 are divisors of 5747)
5747 / 2 = 2873.5 (the remainder is 1, so 2 is not a divisor of 5747)
5747 / 3 = 1915.6666666667 (the remainder is 2, so 3 is not a divisor of 5747)
...
5747 / 74 = 77.662162162162 (the remainder is 49, so 74 is not a divisor of 5747)
5747 / 75 = 76.626666666667 (the remainder is 47, so 75 is not a divisor of 5747)