What are the divisors of 3910?

1, 2, 5, 10, 17, 23, 34, 46, 85, 115, 170, 230, 391, 782, 1955, 3910

There is a total of 16 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 486.

8 even divisors

2, 10, 34, 46, 170, 230, 782, 3910

8 odd divisors

1, 5, 17, 23, 85, 115, 391, 1955

How to compute the divisors of 3910?

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 3910 by each of the numbers from 1 to 3910 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)

3910 / 1 = 3910 (the remainder is 0, so 1 is a divisor of 3910)
3910 / 2 = 1955 (the remainder is 0, so 2 is a divisor of 3910)
3910 / 3 = 1303.3333333333 (the remainder is 1, so 3 is not a divisor of 3910)
...
3910 / 3909 = 1.0002558199028 (the remainder is 1, so 3909 is not a divisor of 3910)
3910 / 3910 = 1 (the remainder is 0, so 3910 is a divisor of 3910)

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 3910 (i.e. 62.529992803454). 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 $\frac{N}{d} = D$ )

3910 / 1 = 3910 (the remainder is 0, so 1 and 3910 are divisors of 3910)
3910 / 2 = 1955 (the remainder is 0, so 2 and 1955 are divisors of 3910)
3910 / 3 = 1303.3333333333 (the remainder is 1, so 3 is not a divisor of 3910)
...
3910 / 61 = 64.098360655738 (the remainder is 6, so 61 is not a divisor of 3910)
3910 / 62 = 63.064516129032 (the remainder is 4, so 62 is not a divisor of 3910)