What are the divisors of 3257?

1, 3257

There is a total of 2 positive divisors.
The sum of these divisors is 3258.
The arithmetic mean is 1629.

2 odd divisors

1, 3257

How to compute the divisors of 3257?

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 3257 by each of the numbers from 1 to 3257 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)

3257 / 1 = 3257 (the remainder is 0, so 1 is a divisor of 3257)
3257 / 2 = 1628.5 (the remainder is 1, so 2 is not a divisor of 3257)
3257 / 3 = 1085.6666666667 (the remainder is 2, so 3 is not a divisor of 3257)
...
3257 / 3256 = 1.0003071253071 (the remainder is 1, so 3256 is not a divisor of 3257)
3257 / 3257 = 1 (the remainder is 0, so 3257 is a divisor of 3257)

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 3257 (i.e. 57.070132293521). 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 $\frac{N}{d} = D$ )

3257 / 1 = 3257 (the remainder is 0, so 1 and 3257 are divisors of 3257)
3257 / 2 = 1628.5 (the remainder is 1, so 2 is not a divisor of 3257)
3257 / 3 = 1085.6666666667 (the remainder is 2, so 3 is not a divisor of 3257)
...
3257 / 56 = 58.160714285714 (the remainder is 9, so 56 is not a divisor of 3257)
3257 / 57 = 57.140350877193 (the remainder is 8, so 57 is not a divisor of 3257)