What are the divisors of 173?

1, 173

There is a total of 2 positive divisors.
The sum of these divisors is 174.
The arithmetic mean is 87.

2 odd divisors

1, 173

How to compute the divisors of 173?

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 173 by each of the numbers from 1 to 173 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)

173 / 1 = 173 (the remainder is 0, so 1 is a divisor of 173)
173 / 2 = 86.5 (the remainder is 1, so 2 is not a divisor of 173)
173 / 3 = 57.666666666667 (the remainder is 2, so 3 is not a divisor of 173)
...
173 / 172 = 1.0058139534884 (the remainder is 1, so 172 is not a divisor of 173)
173 / 173 = 1 (the remainder is 0, so 173 is a divisor of 173)

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 173 (i.e. 13.152946437966). 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 $\frac{N}{d} = D$ )

173 / 1 = 173 (the remainder is 0, so 1 and 173 are divisors of 173)
173 / 2 = 86.5 (the remainder is 1, so 2 is not a divisor of 173)
173 / 3 = 57.666666666667 (the remainder is 2, so 3 is not a divisor of 173)
...
173 / 12 = 14.416666666667 (the remainder is 5, so 12 is not a divisor of 173)
173 / 13 = 13.307692307692 (the remainder is 4, so 13 is not a divisor of 173)