What are the divisors of 3891?

1, 3, 1297, 3891

There is a total of 4 positive divisors.
The sum of these divisors is 5192.
The arithmetic mean is 1298.

4 odd divisors

1, 3, 1297, 3891

How to compute the divisors of 3891?

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 3891 by each of the numbers from 1 to 3891 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)

3891 / 1 = 3891 (the remainder is 0, so 1 is a divisor of 3891)
3891 / 2 = 1945.5 (the remainder is 1, so 2 is not a divisor of 3891)
3891 / 3 = 1297 (the remainder is 0, so 3 is a divisor of 3891)
...
3891 / 3890 = 1.0002570694087 (the remainder is 1, so 3890 is not a divisor of 3891)
3891 / 3891 = 1 (the remainder is 0, so 3891 is a divisor of 3891)

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 3891 (i.e. 62.377880695003). 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 $\frac{N}{d} = D$ )

3891 / 1 = 3891 (the remainder is 0, so 1 and 3891 are divisors of 3891)
3891 / 2 = 1945.5 (the remainder is 1, so 2 is not a divisor of 3891)
3891 / 3 = 1297 (the remainder is 0, so 3 and 1297 are divisors of 3891)
...
3891 / 61 = 63.786885245902 (the remainder is 48, so 61 is not a divisor of 3891)
3891 / 62 = 62.758064516129 (the remainder is 47, so 62 is not a divisor of 3891)