What are the divisors of 911?

1, 911

There is a total of 2 positive divisors.
The sum of these divisors is 912.
The arithmetic mean is 456.

2 odd divisors

1, 911

How to compute the divisors of 911?

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 911 by each of the numbers from 1 to 911 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)

911 / 1 = 911 (the remainder is 0, so 1 is a divisor of 911)
911 / 2 = 455.5 (the remainder is 1, so 2 is not a divisor of 911)
911 / 3 = 303.66666666667 (the remainder is 2, so 3 is not a divisor of 911)
...
911 / 910 = 1.0010989010989 (the remainder is 1, so 910 is not a divisor of 911)
911 / 911 = 1 (the remainder is 0, so 911 is a divisor of 911)

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 911 (i.e. 30.182776545573). 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 $\frac{N}{d} = D$ )

911 / 1 = 911 (the remainder is 0, so 1 and 911 are divisors of 911)
911 / 2 = 455.5 (the remainder is 1, so 2 is not a divisor of 911)
911 / 3 = 303.66666666667 (the remainder is 2, so 3 is not a divisor of 911)
...
911 / 29 = 31.413793103448 (the remainder is 12, so 29 is not a divisor of 911)
911 / 30 = 30.366666666667 (the remainder is 11, so 30 is not a divisor of 911)