What are the divisors of 3302?

1, 2, 13, 26, 127, 254, 1651, 3302

There is a total of 8 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 672.

4 even divisors

2, 26, 254, 3302

4 odd divisors

1, 13, 127, 1651

How to compute the divisors of 3302?

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 3302 by each of the numbers from 1 to 3302 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)

3302 / 1 = 3302 (the remainder is 0, so 1 is a divisor of 3302)
3302 / 2 = 1651 (the remainder is 0, so 2 is a divisor of 3302)
3302 / 3 = 1100.6666666667 (the remainder is 2, so 3 is not a divisor of 3302)
...
3302 / 3301 = 1.0003029385035 (the remainder is 1, so 3301 is not a divisor of 3302)
3302 / 3302 = 1 (the remainder is 0, so 3302 is a divisor of 3302)

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 3302 (i.e. 57.463031594235). 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 $\frac{N}{d} = D$ )

3302 / 1 = 3302 (the remainder is 0, so 1 and 3302 are divisors of 3302)
3302 / 2 = 1651 (the remainder is 0, so 2 and 1651 are divisors of 3302)
3302 / 3 = 1100.6666666667 (the remainder is 2, so 3 is not a divisor of 3302)
...
3302 / 56 = 58.964285714286 (the remainder is 54, so 56 is not a divisor of 3302)
3302 / 57 = 57.929824561404 (the remainder is 53, so 57 is not a divisor of 3302)