What are the divisors of 3771?

1, 3, 9, 419, 1257, 3771

There is a total of 6 positive divisors.
The sum of these divisors is 5460.
The arithmetic mean is 910.

6 odd divisors

1, 3, 9, 419, 1257, 3771

How to compute the divisors of 3771?

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 3771 by each of the numbers from 1 to 3771 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)

3771 / 1 = 3771 (the remainder is 0, so 1 is a divisor of 3771)
3771 / 2 = 1885.5 (the remainder is 1, so 2 is not a divisor of 3771)
3771 / 3 = 1257 (the remainder is 0, so 3 is a divisor of 3771)
...
3771 / 3770 = 1.0002652519894 (the remainder is 1, so 3770 is not a divisor of 3771)
3771 / 3771 = 1 (the remainder is 0, so 3771 is a divisor of 3771)

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 3771 (i.e. 61.408468471376). 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 $\frac{N}{d} = D$ )

3771 / 1 = 3771 (the remainder is 0, so 1 and 3771 are divisors of 3771)
3771 / 2 = 1885.5 (the remainder is 1, so 2 is not a divisor of 3771)
3771 / 3 = 1257 (the remainder is 0, so 3 and 1257 are divisors of 3771)
...
3771 / 60 = 62.85 (the remainder is 51, so 60 is not a divisor of 3771)
3771 / 61 = 61.819672131148 (the remainder is 50, so 61 is not a divisor of 3771)