What are the divisors of 929?

1, 929

There is a total of 2 positive divisors.
The sum of these divisors is 930.
The arithmetic mean is 465.

2 odd divisors

1, 929

How to compute the divisors of 929?

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 929 by each of the numbers from 1 to 929 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)

929 / 1 = 929 (the remainder is 0, so 1 is a divisor of 929)
929 / 2 = 464.5 (the remainder is 1, so 2 is not a divisor of 929)
929 / 3 = 309.66666666667 (the remainder is 2, so 3 is not a divisor of 929)
...
929 / 928 = 1.0010775862069 (the remainder is 1, so 928 is not a divisor of 929)
929 / 929 = 1 (the remainder is 0, so 929 is a divisor of 929)

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 929 (i.e. 30.479501308256). 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 $\frac{N}{d} = D$ )

929 / 1 = 929 (the remainder is 0, so 1 and 929 are divisors of 929)
929 / 2 = 464.5 (the remainder is 1, so 2 is not a divisor of 929)
929 / 3 = 309.66666666667 (the remainder is 2, so 3 is not a divisor of 929)
...
929 / 29 = 32.034482758621 (the remainder is 1, so 29 is not a divisor of 929)
929 / 30 = 30.966666666667 (the remainder is 29, so 30 is not a divisor of 929)