What are the divisors of 3203?

1, 3203

There is a total of 2 positive divisors.
The sum of these divisors is 3204.
The arithmetic mean is 1602.

2 odd divisors

1, 3203

How to compute the divisors of 3203?

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 3203 by each of the numbers from 1 to 3203 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)

3203 / 1 = 3203 (the remainder is 0, so 1 is a divisor of 3203)
3203 / 2 = 1601.5 (the remainder is 1, so 2 is not a divisor of 3203)
3203 / 3 = 1067.6666666667 (the remainder is 2, so 3 is not a divisor of 3203)
...
3203 / 3202 = 1.0003123048095 (the remainder is 1, so 3202 is not a divisor of 3203)
3203 / 3203 = 1 (the remainder is 0, so 3203 is a divisor of 3203)

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 3203 (i.e. 56.595052787324). 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 $\frac{N}{d} = D$ )

3203 / 1 = 3203 (the remainder is 0, so 1 and 3203 are divisors of 3203)
3203 / 2 = 1601.5 (the remainder is 1, so 2 is not a divisor of 3203)
3203 / 3 = 1067.6666666667 (the remainder is 2, so 3 is not a divisor of 3203)
...
3203 / 55 = 58.236363636364 (the remainder is 13, so 55 is not a divisor of 3203)
3203 / 56 = 57.196428571429 (the remainder is 11, so 56 is not a divisor of 3203)