What are the divisors of 3201?

1, 3, 11, 33, 97, 291, 1067, 3201

There is a total of 8 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 588.

8 odd divisors

1, 3, 11, 33, 97, 291, 1067, 3201

How to compute the divisors of 3201?

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 3201 by each of the numbers from 1 to 3201 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)

3201 / 1 = 3201 (the remainder is 0, so 1 is a divisor of 3201)
3201 / 2 = 1600.5 (the remainder is 1, so 2 is not a divisor of 3201)
3201 / 3 = 1067 (the remainder is 0, so 3 is a divisor of 3201)
...
3201 / 3200 = 1.0003125 (the remainder is 1, so 3200 is not a divisor of 3201)
3201 / 3201 = 1 (the remainder is 0, so 3201 is a divisor of 3201)

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 3201 (i.e. 56.577380639263). 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 $\frac{N}{d} = D$ )

3201 / 1 = 3201 (the remainder is 0, so 1 and 3201 are divisors of 3201)
3201 / 2 = 1600.5 (the remainder is 1, so 2 is not a divisor of 3201)
3201 / 3 = 1067 (the remainder is 0, so 3 and 1067 are divisors of 3201)
...
3201 / 55 = 58.2 (the remainder is 11, so 55 is not a divisor of 3201)
3201 / 56 = 57.160714285714 (the remainder is 9, so 56 is not a divisor of 3201)