What are the divisors of 3807?

1, 3, 9, 27, 47, 81, 141, 423, 1269, 3807

There is a total of 10 positive divisors.
The sum of these divisors is 5808.
The arithmetic mean is 580.8.

10 odd divisors

1, 3, 9, 27, 47, 81, 141, 423, 1269, 3807

How to compute the divisors of 3807?

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 3807 by each of the numbers from 1 to 3807 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)

3807 / 1 = 3807 (the remainder is 0, so 1 is a divisor of 3807)
3807 / 2 = 1903.5 (the remainder is 1, so 2 is not a divisor of 3807)
3807 / 3 = 1269 (the remainder is 0, so 3 is a divisor of 3807)
...
3807 / 3806 = 1.0002627430373 (the remainder is 1, so 3806 is not a divisor of 3807)
3807 / 3807 = 1 (the remainder is 0, so 3807 is a divisor of 3807)

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 3807 (i.e. 61.700891403609). 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 $\frac{N}{d} = D$ )

3807 / 1 = 3807 (the remainder is 0, so 1 and 3807 are divisors of 3807)
3807 / 2 = 1903.5 (the remainder is 1, so 2 is not a divisor of 3807)
3807 / 3 = 1269 (the remainder is 0, so 3 and 1269 are divisors of 3807)
...
3807 / 60 = 63.45 (the remainder is 27, so 60 is not a divisor of 3807)
3807 / 61 = 62.409836065574 (the remainder is 25, so 61 is not a divisor of 3807)