What are the divisors of 3783?

1, 3, 13, 39, 97, 291, 1261, 3783

There is a total of 8 positive divisors.
The sum of these divisors is 5488.
The arithmetic mean is 686.

8 odd divisors

1, 3, 13, 39, 97, 291, 1261, 3783

How to compute the divisors of 3783?

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 3783 by each of the numbers from 1 to 3783 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)

3783 / 1 = 3783 (the remainder is 0, so 1 is a divisor of 3783)
3783 / 2 = 1891.5 (the remainder is 1, so 2 is not a divisor of 3783)
3783 / 3 = 1261 (the remainder is 0, so 3 is a divisor of 3783)
...
3783 / 3782 = 1.0002644103649 (the remainder is 1, so 3782 is not a divisor of 3783)
3783 / 3783 = 1 (the remainder is 0, so 3783 is a divisor of 3783)

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 3783 (i.e. 61.506097258727). 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 $\frac{N}{d} = D$ )

3783 / 1 = 3783 (the remainder is 0, so 1 and 3783 are divisors of 3783)
3783 / 2 = 1891.5 (the remainder is 1, so 2 is not a divisor of 3783)
3783 / 3 = 1261 (the remainder is 0, so 3 and 1261 are divisors of 3783)
...
3783 / 60 = 63.05 (the remainder is 3, so 60 is not a divisor of 3783)
3783 / 61 = 62.016393442623 (the remainder is 1, so 61 is not a divisor of 3783)