What are the divisors of 1941?

1, 3, 647, 1941

There is a total of 4 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 648.

4 odd divisors

1, 3, 647, 1941

How to compute the divisors of 1941?

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 1941 by each of the numbers from 1 to 1941 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)

1941 / 1 = 1941 (the remainder is 0, so 1 is a divisor of 1941)
1941 / 2 = 970.5 (the remainder is 1, so 2 is not a divisor of 1941)
1941 / 3 = 647 (the remainder is 0, so 3 is a divisor of 1941)
...
1941 / 1940 = 1.0005154639175 (the remainder is 1, so 1940 is not a divisor of 1941)
1941 / 1941 = 1 (the remainder is 0, so 1941 is a divisor of 1941)

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 1941 (i.e. 44.056781543821). 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 $\frac{N}{d} = D$ )

1941 / 1 = 1941 (the remainder is 0, so 1 and 1941 are divisors of 1941)
1941 / 2 = 970.5 (the remainder is 1, so 2 is not a divisor of 1941)
1941 / 3 = 647 (the remainder is 0, so 3 and 647 are divisors of 1941)
...
1941 / 43 = 45.139534883721 (the remainder is 6, so 43 is not a divisor of 1941)
1941 / 44 = 44.113636363636 (the remainder is 5, so 44 is not a divisor of 1941)