What are the divisors of 932?

1, 2, 4, 233, 466, 932

There is a total of 6 positive divisors.
The sum of these divisors is 1638.
The arithmetic mean is 273.

4 even divisors

2, 4, 466, 932

2 odd divisors

1, 233

How to compute the divisors of 932?

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 932 by each of the numbers from 1 to 932 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)

932 / 1 = 932 (the remainder is 0, so 1 is a divisor of 932)
932 / 2 = 466 (the remainder is 0, so 2 is a divisor of 932)
932 / 3 = 310.66666666667 (the remainder is 2, so 3 is not a divisor of 932)
...
932 / 931 = 1.0010741138561 (the remainder is 1, so 931 is not a divisor of 932)
932 / 932 = 1 (the remainder is 0, so 932 is a divisor of 932)

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 932 (i.e. 30.528675044947). 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 $\frac{N}{d} = D$ )

932 / 1 = 932 (the remainder is 0, so 1 and 932 are divisors of 932)
932 / 2 = 466 (the remainder is 0, so 2 and 466 are divisors of 932)
932 / 3 = 310.66666666667 (the remainder is 2, so 3 is not a divisor of 932)
...
932 / 29 = 32.137931034483 (the remainder is 4, so 29 is not a divisor of 932)
932 / 30 = 31.066666666667 (the remainder is 2, so 30 is not a divisor of 932)