What are the divisors of 3371?

1, 3371

There is a total of 2 positive divisors.
The sum of these divisors is 3372.
The arithmetic mean is 1686.

2 odd divisors

1, 3371

How to compute the divisors of 3371?

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 3371 by each of the numbers from 1 to 3371 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)

3371 / 1 = 3371 (the remainder is 0, so 1 is a divisor of 3371)
3371 / 2 = 1685.5 (the remainder is 1, so 2 is not a divisor of 3371)
3371 / 3 = 1123.6666666667 (the remainder is 2, so 3 is not a divisor of 3371)
...
3371 / 3370 = 1.000296735905 (the remainder is 1, so 3370 is not a divisor of 3371)
3371 / 3371 = 1 (the remainder is 0, so 3371 is a divisor of 3371)

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 3371 (i.e. 58.060313467979). 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 $\frac{N}{d} = D$ )

3371 / 1 = 3371 (the remainder is 0, so 1 and 3371 are divisors of 3371)
3371 / 2 = 1685.5 (the remainder is 1, so 2 is not a divisor of 3371)
3371 / 3 = 1123.6666666667 (the remainder is 2, so 3 is not a divisor of 3371)
...
3371 / 57 = 59.140350877193 (the remainder is 8, so 57 is not a divisor of 3371)
3371 / 58 = 58.120689655172 (the remainder is 7, so 58 is not a divisor of 3371)