What are the divisors of 5749?

1, 5749

There is a total of 2 positive divisors.
The sum of these divisors is 5750.
The arithmetic mean is 2875.

2 odd divisors

1, 5749

How to compute the divisors of 5749?

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 5749 by each of the numbers from 1 to 5749 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)

5749 / 1 = 5749 (the remainder is 0, so 1 is a divisor of 5749)
5749 / 2 = 2874.5 (the remainder is 1, so 2 is not a divisor of 5749)
5749 / 3 = 1916.3333333333 (the remainder is 1, so 3 is not a divisor of 5749)
...
5749 / 5748 = 1.000173973556 (the remainder is 1, so 5748 is not a divisor of 5749)
5749 / 5749 = 1 (the remainder is 0, so 5749 is a divisor of 5749)

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 5749 (i.e. 75.822160349069). 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 $\frac{N}{d} = D$ )

5749 / 1 = 5749 (the remainder is 0, so 1 and 5749 are divisors of 5749)
5749 / 2 = 2874.5 (the remainder is 1, so 2 is not a divisor of 5749)
5749 / 3 = 1916.3333333333 (the remainder is 1, so 3 is not a divisor of 5749)
...
5749 / 74 = 77.689189189189 (the remainder is 51, so 74 is not a divisor of 5749)
5749 / 75 = 76.653333333333 (the remainder is 49, so 75 is not a divisor of 5749)