What are the divisors of 3897?

1, 3, 9, 433, 1299, 3897

There is a total of 6 positive divisors.
The sum of these divisors is 5642.
The arithmetic mean is 940.33333333333.

6 odd divisors

1, 3, 9, 433, 1299, 3897

How to compute the divisors of 3897?

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 3897 by each of the numbers from 1 to 3897 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)

3897 / 1 = 3897 (the remainder is 0, so 1 is a divisor of 3897)
3897 / 2 = 1948.5 (the remainder is 1, so 2 is not a divisor of 3897)
3897 / 3 = 1299 (the remainder is 0, so 3 is a divisor of 3897)
...
3897 / 3896 = 1.0002566735113 (the remainder is 1, so 3896 is not a divisor of 3897)
3897 / 3897 = 1 (the remainder is 0, so 3897 is a divisor of 3897)

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 3897 (i.e. 62.425956140054). 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 $\frac{N}{d} = D$ )

3897 / 1 = 3897 (the remainder is 0, so 1 and 3897 are divisors of 3897)
3897 / 2 = 1948.5 (the remainder is 1, so 2 is not a divisor of 3897)
3897 / 3 = 1299 (the remainder is 0, so 3 and 1299 are divisors of 3897)
...
3897 / 61 = 63.885245901639 (the remainder is 54, so 61 is not a divisor of 3897)
3897 / 62 = 62.854838709677 (the remainder is 53, so 62 is not a divisor of 3897)