What are the divisors of 926?

1, 2, 463, 926

There is a total of 4 positive divisors.
The sum of these divisors is 1392.
The arithmetic mean is 348.

2 even divisors

2, 926

2 odd divisors

1, 463

How to compute the divisors of 926?

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 926 by each of the numbers from 1 to 926 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)

926 / 1 = 926 (the remainder is 0, so 1 is a divisor of 926)
926 / 2 = 463 (the remainder is 0, so 2 is a divisor of 926)
926 / 3 = 308.66666666667 (the remainder is 2, so 3 is not a divisor of 926)
...
926 / 925 = 1.0010810810811 (the remainder is 1, so 925 is not a divisor of 926)
926 / 926 = 1 (the remainder is 0, so 926 is a divisor of 926)

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 926 (i.e. 30.430248109406). 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 $\frac{N}{d} = D$ )

926 / 1 = 926 (the remainder is 0, so 1 and 926 are divisors of 926)
926 / 2 = 463 (the remainder is 0, so 2 and 463 are divisors of 926)
926 / 3 = 308.66666666667 (the remainder is 2, so 3 is not a divisor of 926)
...
926 / 29 = 31.931034482759 (the remainder is 27, so 29 is not a divisor of 926)
926 / 30 = 30.866666666667 (the remainder is 26, so 30 is not a divisor of 926)