What are the divisors of 3862?

1, 2, 1931, 3862

There is a total of 4 positive divisors.
The sum of these divisors is 5796.
The arithmetic mean is 1449.

2 even divisors

2, 3862

2 odd divisors

1, 1931

How to compute the divisors of 3862?

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 3862 by each of the numbers from 1 to 3862 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)

3862 / 1 = 3862 (the remainder is 0, so 1 is a divisor of 3862)
3862 / 2 = 1931 (the remainder is 0, so 2 is a divisor of 3862)
3862 / 3 = 1287.3333333333 (the remainder is 1, so 3 is not a divisor of 3862)
...
3862 / 3861 = 1.000259000259 (the remainder is 1, so 3861 is not a divisor of 3862)
3862 / 3862 = 1 (the remainder is 0, so 3862 is a divisor of 3862)

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 3862 (i.e. 62.144991753157). 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 $\frac{N}{d} = D$ )

3862 / 1 = 3862 (the remainder is 0, so 1 and 3862 are divisors of 3862)
3862 / 2 = 1931 (the remainder is 0, so 2 and 1931 are divisors of 3862)
3862 / 3 = 1287.3333333333 (the remainder is 1, so 3 is not a divisor of 3862)
...
3862 / 61 = 63.311475409836 (the remainder is 19, so 61 is not a divisor of 3862)
3862 / 62 = 62.290322580645 (the remainder is 18, so 62 is not a divisor of 3862)