What are the divisors of 3310?

1, 2, 5, 10, 331, 662, 1655, 3310

There is a total of 8 positive divisors.
The sum of these divisors is 5976.
The arithmetic mean is 747.

4 even divisors

2, 10, 662, 3310

4 odd divisors

1, 5, 331, 1655

How to compute the divisors of 3310?

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 3310 by each of the numbers from 1 to 3310 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)

3310 / 1 = 3310 (the remainder is 0, so 1 is a divisor of 3310)
3310 / 2 = 1655 (the remainder is 0, so 2 is a divisor of 3310)
3310 / 3 = 1103.3333333333 (the remainder is 1, so 3 is not a divisor of 3310)
...
3310 / 3309 = 1.0003022061046 (the remainder is 1, so 3309 is not a divisor of 3310)
3310 / 3310 = 1 (the remainder is 0, so 3310 is a divisor of 3310)

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 3310 (i.e. 57.53259945457). 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 $\frac{N}{d} = D$ )

3310 / 1 = 3310 (the remainder is 0, so 1 and 3310 are divisors of 3310)
3310 / 2 = 1655 (the remainder is 0, so 2 and 1655 are divisors of 3310)
3310 / 3 = 1103.3333333333 (the remainder is 1, so 3 is not a divisor of 3310)
...
3310 / 56 = 59.107142857143 (the remainder is 6, so 56 is not a divisor of 3310)
3310 / 57 = 58.070175438596 (the remainder is 4, so 57 is not a divisor of 3310)