What are the divisors of 3275?

1, 5, 25, 131, 655, 3275

There is a total of 6 positive divisors.
The sum of these divisors is 4092.
The arithmetic mean is 682.

6 odd divisors

1, 5, 25, 131, 655, 3275

How to compute the divisors of 3275?

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 3275 by each of the numbers from 1 to 3275 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)

3275 / 1 = 3275 (the remainder is 0, so 1 is a divisor of 3275)
3275 / 2 = 1637.5 (the remainder is 1, so 2 is not a divisor of 3275)
3275 / 3 = 1091.6666666667 (the remainder is 2, so 3 is not a divisor of 3275)
...
3275 / 3274 = 1.0003054367746 (the remainder is 1, so 3274 is not a divisor of 3275)
3275 / 3275 = 1 (the remainder is 0, so 3275 is a divisor of 3275)

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 3275 (i.e. 57.227615711298). 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 $\frac{N}{d} = D$ )

3275 / 1 = 3275 (the remainder is 0, so 1 and 3275 are divisors of 3275)
3275 / 2 = 1637.5 (the remainder is 1, so 2 is not a divisor of 3275)
3275 / 3 = 1091.6666666667 (the remainder is 2, so 3 is not a divisor of 3275)
...
3275 / 56 = 58.482142857143 (the remainder is 27, so 56 is not a divisor of 3275)
3275 / 57 = 57.456140350877 (the remainder is 26, so 57 is not a divisor of 3275)