What are the divisors of 946?

1, 2, 11, 22, 43, 86, 473, 946

There is a total of 8 positive divisors.
The sum of these divisors is 1584.
The arithmetic mean is 198.

4 even divisors

2, 22, 86, 946

4 odd divisors

1, 11, 43, 473

How to compute the divisors of 946?

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 946 by each of the numbers from 1 to 946 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)

946 / 1 = 946 (the remainder is 0, so 1 is a divisor of 946)
946 / 2 = 473 (the remainder is 0, so 2 is a divisor of 946)
946 / 3 = 315.33333333333 (the remainder is 1, so 3 is not a divisor of 946)
...
946 / 945 = 1.0010582010582 (the remainder is 1, so 945 is not a divisor of 946)
946 / 946 = 1 (the remainder is 0, so 946 is a divisor of 946)

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 946 (i.e. 30.757112998459). 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 $\frac{N}{d} = D$ )

946 / 1 = 946 (the remainder is 0, so 1 and 946 are divisors of 946)
946 / 2 = 473 (the remainder is 0, so 2 and 473 are divisors of 946)
946 / 3 = 315.33333333333 (the remainder is 1, so 3 is not a divisor of 946)
...
946 / 29 = 32.620689655172 (the remainder is 18, so 29 is not a divisor of 946)
946 / 30 = 31.533333333333 (the remainder is 16, so 30 is not a divisor of 946)