What are the divisors of 275?

1, 5, 11, 25, 55, 275

There is a total of 6 positive divisors.
The sum of these divisors is 372.
The arithmetic mean is 62.

6 odd divisors

1, 5, 11, 25, 55, 275

How to compute the divisors of 275?

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 275 by each of the numbers from 1 to 275 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)

275 / 1 = 275 (the remainder is 0, so 1 is a divisor of 275)
275 / 2 = 137.5 (the remainder is 1, so 2 is not a divisor of 275)
275 / 3 = 91.666666666667 (the remainder is 2, so 3 is not a divisor of 275)
...
275 / 274 = 1.0036496350365 (the remainder is 1, so 274 is not a divisor of 275)
275 / 275 = 1 (the remainder is 0, so 275 is a divisor of 275)

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 275 (i.e. 16.583123951777). 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 $\frac{N}{d} = D$ )

275 / 1 = 275 (the remainder is 0, so 1 and 275 are divisors of 275)
275 / 2 = 137.5 (the remainder is 1, so 2 is not a divisor of 275)
275 / 3 = 91.666666666667 (the remainder is 2, so 3 is not a divisor of 275)
...
275 / 15 = 18.333333333333 (the remainder is 5, so 15 is not a divisor of 275)
275 / 16 = 17.1875 (the remainder is 3, so 16 is not a divisor of 275)