What are the divisors of 1915?

1, 5, 383, 1915

There is a total of 4 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 576.

4 odd divisors

1, 5, 383, 1915

How to compute the divisors of 1915?

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 1915 by each of the numbers from 1 to 1915 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)

1915 / 1 = 1915 (the remainder is 0, so 1 is a divisor of 1915)
1915 / 2 = 957.5 (the remainder is 1, so 2 is not a divisor of 1915)
1915 / 3 = 638.33333333333 (the remainder is 1, so 3 is not a divisor of 1915)
...
1915 / 1914 = 1.0005224660397 (the remainder is 1, so 1914 is not a divisor of 1915)
1915 / 1915 = 1 (the remainder is 0, so 1915 is a divisor of 1915)

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 1915 (i.e. 43.760712974082). 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 $\frac{N}{d} = D$ )

1915 / 1 = 1915 (the remainder is 0, so 1 and 1915 are divisors of 1915)
1915 / 2 = 957.5 (the remainder is 1, so 2 is not a divisor of 1915)
1915 / 3 = 638.33333333333 (the remainder is 1, so 3 is not a divisor of 1915)
...
1915 / 42 = 45.595238095238 (the remainder is 25, so 42 is not a divisor of 1915)
1915 / 43 = 44.53488372093 (the remainder is 23, so 43 is not a divisor of 1915)