What are the divisors of 265?

1, 5, 53, 265

There is a total of 4 positive divisors.
The sum of these divisors is 324.
The arithmetic mean is 81.

4 odd divisors

1, 5, 53, 265

How to compute the divisors of 265?

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 265 by each of the numbers from 1 to 265 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)

265 / 1 = 265 (the remainder is 0, so 1 is a divisor of 265)
265 / 2 = 132.5 (the remainder is 1, so 2 is not a divisor of 265)
265 / 3 = 88.333333333333 (the remainder is 1, so 3 is not a divisor of 265)
...
265 / 264 = 1.0037878787879 (the remainder is 1, so 264 is not a divisor of 265)
265 / 265 = 1 (the remainder is 0, so 265 is a divisor of 265)

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 265 (i.e. 16.2788205961). 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 $\frac{N}{d} = D$ )

265 / 1 = 265 (the remainder is 0, so 1 and 265 are divisors of 265)
265 / 2 = 132.5 (the remainder is 1, so 2 is not a divisor of 265)
265 / 3 = 88.333333333333 (the remainder is 1, so 3 is not a divisor of 265)
...
265 / 15 = 17.666666666667 (the remainder is 10, so 15 is not a divisor of 265)
265 / 16 = 16.5625 (the remainder is 9, so 16 is not a divisor of 265)