What are the divisors of 941?

1, 941

There is a total of 2 positive divisors.
The sum of these divisors is 942.
The arithmetic mean is 471.

2 odd divisors

1, 941

How to compute the divisors of 941?

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 941 by each of the numbers from 1 to 941 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)

941 / 1 = 941 (the remainder is 0, so 1 is a divisor of 941)
941 / 2 = 470.5 (the remainder is 1, so 2 is not a divisor of 941)
941 / 3 = 313.66666666667 (the remainder is 2, so 3 is not a divisor of 941)
...
941 / 940 = 1.0010638297872 (the remainder is 1, so 940 is not a divisor of 941)
941 / 941 = 1 (the remainder is 0, so 941 is a divisor of 941)

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 941 (i.e. 30.675723300356). 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 $\frac{N}{d} = D$ )

941 / 1 = 941 (the remainder is 0, so 1 and 941 are divisors of 941)
941 / 2 = 470.5 (the remainder is 1, so 2 is not a divisor of 941)
941 / 3 = 313.66666666667 (the remainder is 2, so 3 is not a divisor of 941)
...
941 / 29 = 32.448275862069 (the remainder is 13, so 29 is not a divisor of 941)
941 / 30 = 31.366666666667 (the remainder is 11, so 30 is not a divisor of 941)