What are the divisors of 934?

1, 2, 467, 934

There is a total of 4 positive divisors.
The sum of these divisors is 1404.
The arithmetic mean is 351.

2 even divisors

2, 934

2 odd divisors

1, 467

How to compute the divisors of 934?

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 934 by each of the numbers from 1 to 934 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)

934 / 1 = 934 (the remainder is 0, so 1 is a divisor of 934)
934 / 2 = 467 (the remainder is 0, so 2 is a divisor of 934)
934 / 3 = 311.33333333333 (the remainder is 1, so 3 is not a divisor of 934)
...
934 / 933 = 1.0010718113612 (the remainder is 1, so 933 is not a divisor of 934)
934 / 934 = 1 (the remainder is 0, so 934 is a divisor of 934)

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 934 (i.e. 30.561413579872). 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 $\frac{N}{d} = D$ )

934 / 1 = 934 (the remainder is 0, so 1 and 934 are divisors of 934)
934 / 2 = 467 (the remainder is 0, so 2 and 467 are divisors of 934)
934 / 3 = 311.33333333333 (the remainder is 1, so 3 is not a divisor of 934)
...
934 / 29 = 32.206896551724 (the remainder is 6, so 29 is not a divisor of 934)
934 / 30 = 31.133333333333 (the remainder is 4, so 30 is not a divisor of 934)