What are the divisors of 3245?

1, 5, 11, 55, 59, 295, 649, 3245

There is a total of 8 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 540.

8 odd divisors

1, 5, 11, 55, 59, 295, 649, 3245

How to compute the divisors of 3245?

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 3245 by each of the numbers from 1 to 3245 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)

3245 / 1 = 3245 (the remainder is 0, so 1 is a divisor of 3245)
3245 / 2 = 1622.5 (the remainder is 1, so 2 is not a divisor of 3245)
3245 / 3 = 1081.6666666667 (the remainder is 2, so 3 is not a divisor of 3245)
...
3245 / 3244 = 1.0003082614057 (the remainder is 1, so 3244 is not a divisor of 3245)
3245 / 3245 = 1 (the remainder is 0, so 3245 is a divisor of 3245)

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 3245 (i.e. 56.964901474504). 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 $\frac{N}{d} = D$ )

3245 / 1 = 3245 (the remainder is 0, so 1 and 3245 are divisors of 3245)
3245 / 2 = 1622.5 (the remainder is 1, so 2 is not a divisor of 3245)
3245 / 3 = 1081.6666666667 (the remainder is 2, so 3 is not a divisor of 3245)
...
3245 / 55 = 59 (the remainder is 0, so 55 and 59 are divisors of 3245)
3245 / 56 = 57.946428571429 (the remainder is 53, so 56 is not a divisor of 3245)