What are the divisors of 3922?

1, 2, 37, 53, 74, 106, 1961, 3922

There is a total of 8 positive divisors.
The sum of these divisors is 6156.
The arithmetic mean is 769.5.

4 even divisors

2, 74, 106, 3922

4 odd divisors

1, 37, 53, 1961

How to compute the divisors of 3922?

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 3922 by each of the numbers from 1 to 3922 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)

3922 / 1 = 3922 (the remainder is 0, so 1 is a divisor of 3922)
3922 / 2 = 1961 (the remainder is 0, so 2 is a divisor of 3922)
3922 / 3 = 1307.3333333333 (the remainder is 1, so 3 is not a divisor of 3922)
...
3922 / 3921 = 1.0002550369804 (the remainder is 1, so 3921 is not a divisor of 3922)
3922 / 3922 = 1 (the remainder is 0, so 3922 is a divisor of 3922)

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 3922 (i.e. 62.625873247405). 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 $\frac{N}{d} = D$ )

3922 / 1 = 3922 (the remainder is 0, so 1 and 3922 are divisors of 3922)
3922 / 2 = 1961 (the remainder is 0, so 2 and 1961 are divisors of 3922)
3922 / 3 = 1307.3333333333 (the remainder is 1, so 3 is not a divisor of 3922)
...
3922 / 61 = 64.295081967213 (the remainder is 18, so 61 is not a divisor of 3922)
3922 / 62 = 63.258064516129 (the remainder is 16, so 62 is not a divisor of 3922)