What are the divisors of 3215?

1, 5, 643, 3215

There is a total of 4 positive divisors.
The sum of these divisors is 3864.
The arithmetic mean is 966.

4 odd divisors

1, 5, 643, 3215

How to compute the divisors of 3215?

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 3215 by each of the numbers from 1 to 3215 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)

3215 / 1 = 3215 (the remainder is 0, so 1 is a divisor of 3215)
3215 / 2 = 1607.5 (the remainder is 1, so 2 is not a divisor of 3215)
3215 / 3 = 1071.6666666667 (the remainder is 2, so 3 is not a divisor of 3215)
...
3215 / 3214 = 1.0003111387679 (the remainder is 1, so 3214 is not a divisor of 3215)
3215 / 3215 = 1 (the remainder is 0, so 3215 is a divisor of 3215)

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 3215 (i.e. 56.700970009339). 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 $\frac{N}{d} = D$ )

3215 / 1 = 3215 (the remainder is 0, so 1 and 3215 are divisors of 3215)
3215 / 2 = 1607.5 (the remainder is 1, so 2 is not a divisor of 3215)
3215 / 3 = 1071.6666666667 (the remainder is 2, so 3 is not a divisor of 3215)
...
3215 / 55 = 58.454545454545 (the remainder is 25, so 55 is not a divisor of 3215)
3215 / 56 = 57.410714285714 (the remainder is 23, so 56 is not a divisor of 3215)