What are the divisors of 3370?

1, 2, 5, 10, 337, 674, 1685, 3370

There is a total of 8 positive divisors.
The sum of these divisors is 6084.
The arithmetic mean is 760.5.

4 even divisors

2, 10, 674, 3370

4 odd divisors

1, 5, 337, 1685

How to compute the divisors of 3370?

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 3370 by each of the numbers from 1 to 3370 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)

3370 / 1 = 3370 (the remainder is 0, so 1 is a divisor of 3370)
3370 / 2 = 1685 (the remainder is 0, so 2 is a divisor of 3370)
3370 / 3 = 1123.3333333333 (the remainder is 1, so 3 is not a divisor of 3370)
...
3370 / 3369 = 1.0002968239834 (the remainder is 1, so 3369 is not a divisor of 3370)
3370 / 3370 = 1 (the remainder is 0, so 3370 is a divisor of 3370)

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 3370 (i.e. 58.0517010948). 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 $\frac{N}{d} = D$ )

3370 / 1 = 3370 (the remainder is 0, so 1 and 3370 are divisors of 3370)
3370 / 2 = 1685 (the remainder is 0, so 2 and 1685 are divisors of 3370)
3370 / 3 = 1123.3333333333 (the remainder is 1, so 3 is not a divisor of 3370)
...
3370 / 57 = 59.122807017544 (the remainder is 7, so 57 is not a divisor of 3370)
3370 / 58 = 58.103448275862 (the remainder is 6, so 58 is not a divisor of 3370)