What are the divisors of 3962?

1, 2, 7, 14, 283, 566, 1981, 3962

There is a total of 8 positive divisors.
The sum of these divisors is 6816.
The arithmetic mean is 852.

4 even divisors

2, 14, 566, 3962

4 odd divisors

1, 7, 283, 1981

How to compute the divisors of 3962?

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 3962 by each of the numbers from 1 to 3962 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)

3962 / 1 = 3962 (the remainder is 0, so 1 is a divisor of 3962)
3962 / 2 = 1981 (the remainder is 0, so 2 is a divisor of 3962)
3962 / 3 = 1320.6666666667 (the remainder is 2, so 3 is not a divisor of 3962)
...
3962 / 3961 = 1.0002524614996 (the remainder is 1, so 3961 is not a divisor of 3962)
3962 / 3962 = 1 (the remainder is 0, so 3962 is a divisor of 3962)

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 3962 (i.e. 62.944419927425). 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 $\frac{N}{d} = D$ )

3962 / 1 = 3962 (the remainder is 0, so 1 and 3962 are divisors of 3962)
3962 / 2 = 1981 (the remainder is 0, so 2 and 1981 are divisors of 3962)
3962 / 3 = 1320.6666666667 (the remainder is 2, so 3 is not a divisor of 3962)
...
3962 / 61 = 64.950819672131 (the remainder is 58, so 61 is not a divisor of 3962)
3962 / 62 = 63.903225806452 (the remainder is 56, so 62 is not a divisor of 3962)