What are the divisors of 3790?

1, 2, 5, 10, 379, 758, 1895, 3790

There is a total of 8 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 855.

4 even divisors

2, 10, 758, 3790

4 odd divisors

1, 5, 379, 1895

How to compute the divisors of 3790?

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 3790 by each of the numbers from 1 to 3790 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)

3790 / 1 = 3790 (the remainder is 0, so 1 is a divisor of 3790)
3790 / 2 = 1895 (the remainder is 0, so 2 is a divisor of 3790)
3790 / 3 = 1263.3333333333 (the remainder is 1, so 3 is not a divisor of 3790)
...
3790 / 3789 = 1.0002639218791 (the remainder is 1, so 3789 is not a divisor of 3790)
3790 / 3790 = 1 (the remainder is 0, so 3790 is a divisor of 3790)

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 3790 (i.e. 61.562975886486). 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 $\frac{N}{d} = D$ )

3790 / 1 = 3790 (the remainder is 0, so 1 and 3790 are divisors of 3790)
3790 / 2 = 1895 (the remainder is 0, so 2 and 1895 are divisors of 3790)
3790 / 3 = 1263.3333333333 (the remainder is 1, so 3 is not a divisor of 3790)
...
3790 / 60 = 63.166666666667 (the remainder is 10, so 60 is not a divisor of 3790)
3790 / 61 = 62.131147540984 (the remainder is 8, so 61 is not a divisor of 3790)