What are the divisors of 3372?

1, 2, 3, 4, 6, 12, 281, 562, 843, 1124, 1686, 3372

There is a total of 12 positive divisors.
The sum of these divisors is 7896.
The arithmetic mean is 658.

8 even divisors

2, 4, 6, 12, 562, 1124, 1686, 3372

4 odd divisors

1, 3, 281, 843

How to compute the divisors of 3372?

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 3372 by each of the numbers from 1 to 3372 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)

3372 / 1 = 3372 (the remainder is 0, so 1 is a divisor of 3372)
3372 / 2 = 1686 (the remainder is 0, so 2 is a divisor of 3372)
3372 / 3 = 1124 (the remainder is 0, so 3 is a divisor of 3372)
...
3372 / 3371 = 1.000296647879 (the remainder is 1, so 3371 is not a divisor of 3372)
3372 / 3372 = 1 (the remainder is 0, so 3372 is a divisor of 3372)

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 3372 (i.e. 58.068924563832). 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 $\frac{N}{d} = D$ )

3372 / 1 = 3372 (the remainder is 0, so 1 and 3372 are divisors of 3372)
3372 / 2 = 1686 (the remainder is 0, so 2 and 1686 are divisors of 3372)
3372 / 3 = 1124 (the remainder is 0, so 3 and 1124 are divisors of 3372)
...
3372 / 57 = 59.157894736842 (the remainder is 9, so 57 is not a divisor of 3372)
3372 / 58 = 58.137931034483 (the remainder is 8, so 58 is not a divisor of 3372)