What are the divisors of 3353?

1, 7, 479, 3353

There is a total of 4 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 960.

4 odd divisors

1, 7, 479, 3353

How to compute the divisors of 3353?

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 3353 by each of the numbers from 1 to 3353 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)

3353 / 1 = 3353 (the remainder is 0, so 1 is a divisor of 3353)
3353 / 2 = 1676.5 (the remainder is 1, so 2 is not a divisor of 3353)
3353 / 3 = 1117.6666666667 (the remainder is 2, so 3 is not a divisor of 3353)
...
3353 / 3352 = 1.0002983293556 (the remainder is 1, so 3352 is not a divisor of 3353)
3353 / 3353 = 1 (the remainder is 0, so 3353 is a divisor of 3353)

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 3353 (i.e. 57.905094767214). 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 $\frac{N}{d} = D$ )

3353 / 1 = 3353 (the remainder is 0, so 1 and 3353 are divisors of 3353)
3353 / 2 = 1676.5 (the remainder is 1, so 2 is not a divisor of 3353)
3353 / 3 = 1117.6666666667 (the remainder is 2, so 3 is not a divisor of 3353)
...
3353 / 56 = 59.875 (the remainder is 49, so 56 is not a divisor of 3353)
3353 / 57 = 58.824561403509 (the remainder is 47, so 57 is not a divisor of 3353)