What are the divisors of 907?

1, 907

There is a total of 2 positive divisors.
The sum of these divisors is 908.
The arithmetic mean is 454.

2 odd divisors

1, 907

How to compute the divisors of 907?

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 907 by each of the numbers from 1 to 907 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)

907 / 1 = 907 (the remainder is 0, so 1 is a divisor of 907)
907 / 2 = 453.5 (the remainder is 1, so 2 is not a divisor of 907)
907 / 3 = 302.33333333333 (the remainder is 1, so 3 is not a divisor of 907)
...
907 / 906 = 1.0011037527594 (the remainder is 1, so 906 is not a divisor of 907)
907 / 907 = 1 (the remainder is 0, so 907 is a divisor of 907)

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 907 (i.e. 30.116440692751). 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 $\frac{N}{d} = D$ )

907 / 1 = 907 (the remainder is 0, so 1 and 907 are divisors of 907)
907 / 2 = 453.5 (the remainder is 1, so 2 is not a divisor of 907)
907 / 3 = 302.33333333333 (the remainder is 1, so 3 is not a divisor of 907)
...
907 / 29 = 31.275862068966 (the remainder is 8, so 29 is not a divisor of 907)
907 / 30 = 30.233333333333 (the remainder is 7, so 30 is not a divisor of 907)