What are the divisors of 3835?

1, 5, 13, 59, 65, 295, 767, 3835

There is a total of 8 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 630.

8 odd divisors

1, 5, 13, 59, 65, 295, 767, 3835

How to compute the divisors of 3835?

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 3835 by each of the numbers from 1 to 3835 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)

3835 / 1 = 3835 (the remainder is 0, so 1 is a divisor of 3835)
3835 / 2 = 1917.5 (the remainder is 1, so 2 is not a divisor of 3835)
3835 / 3 = 1278.3333333333 (the remainder is 1, so 3 is not a divisor of 3835)
...
3835 / 3834 = 1.0002608242045 (the remainder is 1, so 3834 is not a divisor of 3835)
3835 / 3835 = 1 (the remainder is 0, so 3835 is a divisor of 3835)

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 3835 (i.e. 61.927376821564). 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 $\frac{N}{d} = D$ )

3835 / 1 = 3835 (the remainder is 0, so 1 and 3835 are divisors of 3835)
3835 / 2 = 1917.5 (the remainder is 1, so 2 is not a divisor of 3835)
3835 / 3 = 1278.3333333333 (the remainder is 1, so 3 is not a divisor of 3835)
...
3835 / 60 = 63.916666666667 (the remainder is 55, so 60 is not a divisor of 3835)
3835 / 61 = 62.868852459016 (the remainder is 53, so 61 is not a divisor of 3835)