What are the divisors of 1913?

1, 1913

There is a total of 2 positive divisors.
The sum of these divisors is 1914.
The arithmetic mean is 957.

2 odd divisors

1, 1913

How to compute the divisors of 1913?

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 1913 by each of the numbers from 1 to 1913 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)

1913 / 1 = 1913 (the remainder is 0, so 1 is a divisor of 1913)
1913 / 2 = 956.5 (the remainder is 1, so 2 is not a divisor of 1913)
1913 / 3 = 637.66666666667 (the remainder is 2, so 3 is not a divisor of 1913)
...
1913 / 1912 = 1.0005230125523 (the remainder is 1, so 1912 is not a divisor of 1913)
1913 / 1913 = 1 (the remainder is 0, so 1913 is a divisor of 1913)

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 1913 (i.e. 43.737855457258). 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 $\frac{N}{d} = D$ )

1913 / 1 = 1913 (the remainder is 0, so 1 and 1913 are divisors of 1913)
1913 / 2 = 956.5 (the remainder is 1, so 2 is not a divisor of 1913)
1913 / 3 = 637.66666666667 (the remainder is 2, so 3 is not a divisor of 1913)
...
1913 / 42 = 45.547619047619 (the remainder is 23, so 42 is not a divisor of 1913)
1913 / 43 = 44.488372093023 (the remainder is 21, so 43 is not a divisor of 1913)