What are the divisors of 175?

1, 5, 7, 25, 35, 175

There is a total of 6 positive divisors.
The sum of these divisors is 248.
The arithmetic mean is 41.333333333333.

6 odd divisors

1, 5, 7, 25, 35, 175

How to compute the divisors of 175?

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 175 by each of the numbers from 1 to 175 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)

175 / 1 = 175 (the remainder is 0, so 1 is a divisor of 175)
175 / 2 = 87.5 (the remainder is 1, so 2 is not a divisor of 175)
175 / 3 = 58.333333333333 (the remainder is 1, so 3 is not a divisor of 175)
...
175 / 174 = 1.0057471264368 (the remainder is 1, so 174 is not a divisor of 175)
175 / 175 = 1 (the remainder is 0, so 175 is a divisor of 175)

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 175 (i.e. 13.228756555323). 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 $\frac{N}{d} = D$ )

175 / 1 = 175 (the remainder is 0, so 1 and 175 are divisors of 175)
175 / 2 = 87.5 (the remainder is 1, so 2 is not a divisor of 175)
175 / 3 = 58.333333333333 (the remainder is 1, so 3 is not a divisor of 175)
...
175 / 12 = 14.583333333333 (the remainder is 7, so 12 is not a divisor of 175)
175 / 13 = 13.461538461538 (the remainder is 6, so 13 is not a divisor of 175)