What are the divisors of 3170?

1, 2, 5, 10, 317, 634, 1585, 3170

There is a total of 8 positive divisors.
The sum of these divisors is 5724.
The arithmetic mean is 715.5.

4 even divisors

2, 10, 634, 3170

4 odd divisors

1, 5, 317, 1585

How to compute the divisors of 3170?

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 3170 by each of the numbers from 1 to 3170 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)

3170 / 1 = 3170 (the remainder is 0, so 1 is a divisor of 3170)
3170 / 2 = 1585 (the remainder is 0, so 2 is a divisor of 3170)
3170 / 3 = 1056.6666666667 (the remainder is 2, so 3 is not a divisor of 3170)
...
3170 / 3169 = 1.000315556958 (the remainder is 1, so 3169 is not a divisor of 3170)
3170 / 3170 = 1 (the remainder is 0, so 3170 is a divisor of 3170)

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 3170 (i.e. 56.302753041037). 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 $\frac{N}{d} = D$ )

3170 / 1 = 3170 (the remainder is 0, so 1 and 3170 are divisors of 3170)
3170 / 2 = 1585 (the remainder is 0, so 2 and 1585 are divisors of 3170)
3170 / 3 = 1056.6666666667 (the remainder is 2, so 3 is not a divisor of 3170)
...
3170 / 55 = 57.636363636364 (the remainder is 35, so 55 is not a divisor of 3170)
3170 / 56 = 56.607142857143 (the remainder is 34, so 56 is not a divisor of 3170)