What are the divisors of 3938?

1, 2, 11, 22, 179, 358, 1969, 3938

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

4 even divisors

2, 22, 358, 3938

4 odd divisors

1, 11, 179, 1969

How to compute the divisors of 3938?

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 3938 by each of the numbers from 1 to 3938 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)

3938 / 1 = 3938 (the remainder is 0, so 1 is a divisor of 3938)
3938 / 2 = 1969 (the remainder is 0, so 2 is a divisor of 3938)
3938 / 3 = 1312.6666666667 (the remainder is 2, so 3 is not a divisor of 3938)
...
3938 / 3937 = 1.000254000508 (the remainder is 1, so 3937 is not a divisor of 3938)
3938 / 3938 = 1 (the remainder is 0, so 3938 is a divisor of 3938)

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 3938 (i.e. 62.753485958949). 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 $\frac{N}{d} = D$ )

3938 / 1 = 3938 (the remainder is 0, so 1 and 3938 are divisors of 3938)
3938 / 2 = 1969 (the remainder is 0, so 2 and 1969 are divisors of 3938)
3938 / 3 = 1312.6666666667 (the remainder is 2, so 3 is not a divisor of 3938)
...
3938 / 61 = 64.55737704918 (the remainder is 34, so 61 is not a divisor of 3938)
3938 / 62 = 63.516129032258 (the remainder is 32, so 62 is not a divisor of 3938)