What are the divisors of 3733?

1, 3733

There is a total of 2 positive divisors.
The sum of these divisors is 3734.
The arithmetic mean is 1867.

2 odd divisors

1, 3733

How to compute the divisors of 3733?

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 3733 by each of the numbers from 1 to 3733 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)

3733 / 1 = 3733 (the remainder is 0, so 1 is a divisor of 3733)
3733 / 2 = 1866.5 (the remainder is 1, so 2 is not a divisor of 3733)
3733 / 3 = 1244.3333333333 (the remainder is 1, so 3 is not a divisor of 3733)
...
3733 / 3732 = 1.0002679528403 (the remainder is 1, so 3732 is not a divisor of 3733)
3733 / 3733 = 1 (the remainder is 0, so 3733 is a divisor of 3733)

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 3733 (i.e. 61.098281481561). 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 $\frac{N}{d} = D$ )

3733 / 1 = 3733 (the remainder is 0, so 1 and 3733 are divisors of 3733)
3733 / 2 = 1866.5 (the remainder is 1, so 2 is not a divisor of 3733)
3733 / 3 = 1244.3333333333 (the remainder is 1, so 3 is not a divisor of 3733)
...
3733 / 60 = 62.216666666667 (the remainder is 13, so 60 is not a divisor of 3733)
3733 / 61 = 61.196721311475 (the remainder is 12, so 61 is not a divisor of 3733)