What are the divisors of 937?

1, 937

There is a total of 2 positive divisors.
The sum of these divisors is 938.
The arithmetic mean is 469.

2 odd divisors

1, 937

How to compute the divisors of 937?

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 937 by each of the numbers from 1 to 937 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)

937 / 1 = 937 (the remainder is 0, so 1 is a divisor of 937)
937 / 2 = 468.5 (the remainder is 1, so 2 is not a divisor of 937)
937 / 3 = 312.33333333333 (the remainder is 1, so 3 is not a divisor of 937)
...
937 / 936 = 1.0010683760684 (the remainder is 1, so 936 is not a divisor of 937)
937 / 937 = 1 (the remainder is 0, so 937 is a divisor of 937)

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 937 (i.e. 30.610455730028). 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 $\frac{N}{d} = D$ )

937 / 1 = 937 (the remainder is 0, so 1 and 937 are divisors of 937)
937 / 2 = 468.5 (the remainder is 1, so 2 is not a divisor of 937)
937 / 3 = 312.33333333333 (the remainder is 1, so 3 is not a divisor of 937)
...
937 / 29 = 32.310344827586 (the remainder is 9, so 29 is not a divisor of 937)
937 / 30 = 31.233333333333 (the remainder is 7, so 30 is not a divisor of 937)