What are the divisors of 3683?

1, 29, 127, 3683

There is a total of 4 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 960.

4 odd divisors

1, 29, 127, 3683

How to compute the divisors of 3683?

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 3683 by each of the numbers from 1 to 3683 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)

3683 / 1 = 3683 (the remainder is 0, so 1 is a divisor of 3683)
3683 / 2 = 1841.5 (the remainder is 1, so 2 is not a divisor of 3683)
3683 / 3 = 1227.6666666667 (the remainder is 2, so 3 is not a divisor of 3683)
...
3683 / 3682 = 1.0002715915263 (the remainder is 1, so 3682 is not a divisor of 3683)
3683 / 3683 = 1 (the remainder is 0, so 3683 is a divisor of 3683)

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 3683 (i.e. 60.687725282795). 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 $\frac{N}{d} = D$ )

3683 / 1 = 3683 (the remainder is 0, so 1 and 3683 are divisors of 3683)
3683 / 2 = 1841.5 (the remainder is 1, so 2 is not a divisor of 3683)
3683 / 3 = 1227.6666666667 (the remainder is 2, so 3 is not a divisor of 3683)
...
3683 / 59 = 62.423728813559 (the remainder is 25, so 59 is not a divisor of 3683)
3683 / 60 = 61.383333333333 (the remainder is 23, so 60 is not a divisor of 3683)