What are the divisors of 3853?

1, 3853

There is a total of 2 positive divisors.
The sum of these divisors is 3854.
The arithmetic mean is 1927.

2 odd divisors

1, 3853

How to compute the divisors of 3853?

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 3853 by each of the numbers from 1 to 3853 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)

3853 / 1 = 3853 (the remainder is 0, so 1 is a divisor of 3853)
3853 / 2 = 1926.5 (the remainder is 1, so 2 is not a divisor of 3853)
3853 / 3 = 1284.3333333333 (the remainder is 1, so 3 is not a divisor of 3853)
...
3853 / 3852 = 1.0002596053998 (the remainder is 1, so 3852 is not a divisor of 3853)
3853 / 3853 = 1 (the remainder is 0, so 3853 is a divisor of 3853)

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 3853 (i.e. 62.072538211354). 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 $\frac{N}{d} = D$ )

3853 / 1 = 3853 (the remainder is 0, so 1 and 3853 are divisors of 3853)
3853 / 2 = 1926.5 (the remainder is 1, so 2 is not a divisor of 3853)
3853 / 3 = 1284.3333333333 (the remainder is 1, so 3 is not a divisor of 3853)
...
3853 / 61 = 63.16393442623 (the remainder is 10, so 61 is not a divisor of 3853)
3853 / 62 = 62.145161290323 (the remainder is 9, so 62 is not a divisor of 3853)