What are the divisors of 3711?

1, 3, 1237, 3711

There is a total of 4 positive divisors.
The sum of these divisors is 4952.
The arithmetic mean is 1238.

4 odd divisors

1, 3, 1237, 3711

How to compute the divisors of 3711?

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 3711 by each of the numbers from 1 to 3711 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)

3711 / 1 = 3711 (the remainder is 0, so 1 is a divisor of 3711)
3711 / 2 = 1855.5 (the remainder is 1, so 2 is not a divisor of 3711)
3711 / 3 = 1237 (the remainder is 0, so 3 is a divisor of 3711)
...
3711 / 3710 = 1.000269541779 (the remainder is 1, so 3710 is not a divisor of 3711)
3711 / 3711 = 1 (the remainder is 0, so 3711 is a divisor of 3711)

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 3711 (i.e. 60.917977642072). 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 $\frac{N}{d} = D$ )

3711 / 1 = 3711 (the remainder is 0, so 1 and 3711 are divisors of 3711)
3711 / 2 = 1855.5 (the remainder is 1, so 2 is not a divisor of 3711)
3711 / 3 = 1237 (the remainder is 0, so 3 and 1237 are divisors of 3711)
...
3711 / 59 = 62.898305084746 (the remainder is 53, so 59 is not a divisor of 3711)
3711 / 60 = 61.85 (the remainder is 51, so 60 is not a divisor of 3711)