What are the divisors of 170?

1, 2, 5, 10, 17, 34, 85, 170

There is a total of 8 positive divisors.
The sum of these divisors is 324.
The arithmetic mean is 40.5.

4 even divisors

2, 10, 34, 170

4 odd divisors

1, 5, 17, 85

How to compute the divisors of 170?

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 170 by each of the numbers from 1 to 170 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)

170 / 1 = 170 (the remainder is 0, so 1 is a divisor of 170)
170 / 2 = 85 (the remainder is 0, so 2 is a divisor of 170)
170 / 3 = 56.666666666667 (the remainder is 2, so 3 is not a divisor of 170)
...
170 / 169 = 1.0059171597633 (the remainder is 1, so 169 is not a divisor of 170)
170 / 170 = 1 (the remainder is 0, so 170 is a divisor of 170)

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 170 (i.e. 13.038404810405). 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 $\frac{N}{d} = D$ )

170 / 1 = 170 (the remainder is 0, so 1 and 170 are divisors of 170)
170 / 2 = 85 (the remainder is 0, so 2 and 85 are divisors of 170)
170 / 3 = 56.666666666667 (the remainder is 2, so 3 is not a divisor of 170)
...
170 / 12 = 14.166666666667 (the remainder is 2, so 12 is not a divisor of 170)
170 / 13 = 13.076923076923 (the remainder is 1, so 13 is not a divisor of 170)