What are the divisors of 295?

1, 5, 59, 295

There is a total of 4 positive divisors.
The sum of these divisors is 360.
The arithmetic mean is 90.

4 odd divisors

1, 5, 59, 295

How to compute the divisors of 295?

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 295 by each of the numbers from 1 to 295 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)

295 / 1 = 295 (the remainder is 0, so 1 is a divisor of 295)
295 / 2 = 147.5 (the remainder is 1, so 2 is not a divisor of 295)
295 / 3 = 98.333333333333 (the remainder is 1, so 3 is not a divisor of 295)
...
295 / 294 = 1.0034013605442 (the remainder is 1, so 294 is not a divisor of 295)
295 / 295 = 1 (the remainder is 0, so 295 is a divisor of 295)

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 295 (i.e. 17.175564037318). 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 $\frac{N}{d} = D$ )

295 / 1 = 295 (the remainder is 0, so 1 and 295 are divisors of 295)
295 / 2 = 147.5 (the remainder is 1, so 2 is not a divisor of 295)
295 / 3 = 98.333333333333 (the remainder is 1, so 3 is not a divisor of 295)
...
295 / 16 = 18.4375 (the remainder is 7, so 16 is not a divisor of 295)
295 / 17 = 17.352941176471 (the remainder is 6, so 17 is not a divisor of 295)