What are the divisors of 3857?

1, 7, 19, 29, 133, 203, 551, 3857

There is a total of 8 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 600.

8 odd divisors

1, 7, 19, 29, 133, 203, 551, 3857

How to compute the divisors of 3857?

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 3857 by each of the numbers from 1 to 3857 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)

3857 / 1 = 3857 (the remainder is 0, so 1 is a divisor of 3857)
3857 / 2 = 1928.5 (the remainder is 1, so 2 is not a divisor of 3857)
3857 / 3 = 1285.6666666667 (the remainder is 2, so 3 is not a divisor of 3857)
...
3857 / 3856 = 1.0002593360996 (the remainder is 1, so 3856 is not a divisor of 3857)
3857 / 3857 = 1 (the remainder is 0, so 3857 is a divisor of 3857)

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 3857 (i.e. 62.104750220897). 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 $\frac{N}{d} = D$ )

3857 / 1 = 3857 (the remainder is 0, so 1 and 3857 are divisors of 3857)
3857 / 2 = 1928.5 (the remainder is 1, so 2 is not a divisor of 3857)
3857 / 3 = 1285.6666666667 (the remainder is 2, so 3 is not a divisor of 3857)
...
3857 / 61 = 63.229508196721 (the remainder is 14, so 61 is not a divisor of 3857)
3857 / 62 = 62.209677419355 (the remainder is 13, so 62 is not a divisor of 3857)