What are the divisors of 3308?

1, 2, 4, 827, 1654, 3308

There is a total of 6 positive divisors.
The sum of these divisors is 5796.
The arithmetic mean is 966.

4 even divisors

2, 4, 1654, 3308

2 odd divisors

1, 827

How to compute the divisors of 3308?

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 3308 by each of the numbers from 1 to 3308 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)

3308 / 1 = 3308 (the remainder is 0, so 1 is a divisor of 3308)
3308 / 2 = 1654 (the remainder is 0, so 2 is a divisor of 3308)
3308 / 3 = 1102.6666666667 (the remainder is 2, so 3 is not a divisor of 3308)
...
3308 / 3307 = 1.0003023888721 (the remainder is 1, so 3307 is not a divisor of 3308)
3308 / 3308 = 1 (the remainder is 0, so 3308 is a divisor of 3308)

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 3308 (i.e. 57.515215378194). 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 $\frac{N}{d} = D$ )

3308 / 1 = 3308 (the remainder is 0, so 1 and 3308 are divisors of 3308)
3308 / 2 = 1654 (the remainder is 0, so 2 and 1654 are divisors of 3308)
3308 / 3 = 1102.6666666667 (the remainder is 2, so 3 is not a divisor of 3308)
...
3308 / 56 = 59.071428571429 (the remainder is 4, so 56 is not a divisor of 3308)
3308 / 57 = 58.035087719298 (the remainder is 2, so 57 is not a divisor of 3308)