What are the divisors of 1916?

1, 2, 4, 479, 958, 1916

There is a total of 6 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 560.

4 even divisors

2, 4, 958, 1916

2 odd divisors

1, 479

How to compute the divisors of 1916?

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 1916 by each of the numbers from 1 to 1916 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)

1916 / 1 = 1916 (the remainder is 0, so 1 is a divisor of 1916)
1916 / 2 = 958 (the remainder is 0, so 2 is a divisor of 1916)
1916 / 3 = 638.66666666667 (the remainder is 2, so 3 is not a divisor of 1916)
...
1916 / 1915 = 1.0005221932115 (the remainder is 1, so 1915 is not a divisor of 1916)
1916 / 1916 = 1 (the remainder is 0, so 1916 is a divisor of 1916)

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 1916 (i.e. 43.772137256479). 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 $\frac{N}{d} = D$ )

1916 / 1 = 1916 (the remainder is 0, so 1 and 1916 are divisors of 1916)
1916 / 2 = 958 (the remainder is 0, so 2 and 958 are divisors of 1916)
1916 / 3 = 638.66666666667 (the remainder is 2, so 3 is not a divisor of 1916)
...
1916 / 42 = 45.619047619048 (the remainder is 26, so 42 is not a divisor of 1916)
1916 / 43 = 44.558139534884 (the remainder is 24, so 43 is not a divisor of 1916)