What are the divisors of 3357?

1, 3, 9, 373, 1119, 3357

There is a total of 6 positive divisors.
The sum of these divisors is 4862.
The arithmetic mean is 810.33333333333.

6 odd divisors

1, 3, 9, 373, 1119, 3357

How to compute the divisors of 3357?

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 3357 by each of the numbers from 1 to 3357 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)

3357 / 1 = 3357 (the remainder is 0, so 1 is a divisor of 3357)
3357 / 2 = 1678.5 (the remainder is 1, so 2 is not a divisor of 3357)
3357 / 3 = 1119 (the remainder is 0, so 3 is a divisor of 3357)
...
3357 / 3356 = 1.0002979737783 (the remainder is 1, so 3356 is not a divisor of 3357)
3357 / 3357 = 1 (the remainder is 0, so 3357 is a divisor of 3357)

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 3357 (i.e. 57.939623747484). 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 $\frac{N}{d} = D$ )

3357 / 1 = 3357 (the remainder is 0, so 1 and 3357 are divisors of 3357)
3357 / 2 = 1678.5 (the remainder is 1, so 2 is not a divisor of 3357)
3357 / 3 = 1119 (the remainder is 0, so 3 and 1119 are divisors of 3357)
...
3357 / 56 = 59.946428571429 (the remainder is 53, so 56 is not a divisor of 3357)
3357 / 57 = 58.894736842105 (the remainder is 51, so 57 is not a divisor of 3357)