What are the divisors of 3271?

1, 3271

There is a total of 2 positive divisors.
The sum of these divisors is 3272.
The arithmetic mean is 1636.

2 odd divisors

1, 3271

How to compute the divisors of 3271?

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 3271 by each of the numbers from 1 to 3271 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)

3271 / 1 = 3271 (the remainder is 0, so 1 is a divisor of 3271)
3271 / 2 = 1635.5 (the remainder is 1, so 2 is not a divisor of 3271)
3271 / 3 = 1090.3333333333 (the remainder is 1, so 3 is not a divisor of 3271)
...
3271 / 3270 = 1.0003058103976 (the remainder is 1, so 3270 is not a divisor of 3271)
3271 / 3271 = 1 (the remainder is 0, so 3271 is a divisor of 3271)

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 3271 (i.e. 57.192656871315). 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 $\frac{N}{d} = D$ )

3271 / 1 = 3271 (the remainder is 0, so 1 and 3271 are divisors of 3271)
3271 / 2 = 1635.5 (the remainder is 1, so 2 is not a divisor of 3271)
3271 / 3 = 1090.3333333333 (the remainder is 1, so 3 is not a divisor of 3271)
...
3271 / 56 = 58.410714285714 (the remainder is 23, so 56 is not a divisor of 3271)
3271 / 57 = 57.385964912281 (the remainder is 22, so 57 is not a divisor of 3271)