What are the divisors of 3250?

1, 2, 5, 10, 13, 25, 26, 50, 65, 125, 130, 250, 325, 650, 1625, 3250

There is a total of 16 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 409.5.

8 even divisors

2, 10, 26, 50, 130, 250, 650, 3250

8 odd divisors

1, 5, 13, 25, 65, 125, 325, 1625

How to compute the divisors of 3250?

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 3250 by each of the numbers from 1 to 3250 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)

3250 / 1 = 3250 (the remainder is 0, so 1 is a divisor of 3250)
3250 / 2 = 1625 (the remainder is 0, so 2 is a divisor of 3250)
3250 / 3 = 1083.3333333333 (the remainder is 1, so 3 is not a divisor of 3250)
...
3250 / 3249 = 1.0003077870114 (the remainder is 1, so 3249 is not a divisor of 3250)
3250 / 3250 = 1 (the remainder is 0, so 3250 is a divisor of 3250)

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 3250 (i.e. 57.008771254957). 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 $\frac{N}{d} = D$ )

3250 / 1 = 3250 (the remainder is 0, so 1 and 3250 are divisors of 3250)
3250 / 2 = 1625 (the remainder is 0, so 2 and 1625 are divisors of 3250)
3250 / 3 = 1083.3333333333 (the remainder is 1, so 3 is not a divisor of 3250)
...
3250 / 56 = 58.035714285714 (the remainder is 2, so 56 is not a divisor of 3250)
3250 / 57 = 57.017543859649 (the remainder is 1, so 57 is not a divisor of 3250)