What are the divisors of 944?

1, 2, 4, 8, 16, 59, 118, 236, 472, 944

There is a total of 10 positive divisors.
The sum of these divisors is 1860.
The arithmetic mean is 186.

8 even divisors

2, 4, 8, 16, 118, 236, 472, 944

2 odd divisors

1, 59

How to compute the divisors of 944?

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 944 by each of the numbers from 1 to 944 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)

944 / 1 = 944 (the remainder is 0, so 1 is a divisor of 944)
944 / 2 = 472 (the remainder is 0, so 2 is a divisor of 944)
944 / 3 = 314.66666666667 (the remainder is 2, so 3 is not a divisor of 944)
...
944 / 943 = 1.0010604453871 (the remainder is 1, so 943 is not a divisor of 944)
944 / 944 = 1 (the remainder is 0, so 944 is a divisor of 944)

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 944 (i.e. 30.724582991474). 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 $\frac{N}{d} = D$ )

944 / 1 = 944 (the remainder is 0, so 1 and 944 are divisors of 944)
944 / 2 = 472 (the remainder is 0, so 2 and 472 are divisors of 944)
944 / 3 = 314.66666666667 (the remainder is 2, so 3 is not a divisor of 944)
...
944 / 29 = 32.551724137931 (the remainder is 16, so 29 is not a divisor of 944)
944 / 30 = 31.466666666667 (the remainder is 14, so 30 is not a divisor of 944)