What are the divisors of 1912?

1, 2, 4, 8, 239, 478, 956, 1912

There is a total of 8 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 450.

6 even divisors

2, 4, 8, 478, 956, 1912

2 odd divisors

1, 239

How to compute the divisors of 1912?

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 1912 by each of the numbers from 1 to 1912 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)

1912 / 1 = 1912 (the remainder is 0, so 1 is a divisor of 1912)
1912 / 2 = 956 (the remainder is 0, so 2 is a divisor of 1912)
1912 / 3 = 637.33333333333 (the remainder is 1, so 3 is not a divisor of 1912)
...
1912 / 1911 = 1.0005232862376 (the remainder is 1, so 1911 is not a divisor of 1912)
1912 / 1912 = 1 (the remainder is 0, so 1912 is a divisor of 1912)

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 1912 (i.e. 43.726422218151). 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 $\frac{N}{d} = D$ )

1912 / 1 = 1912 (the remainder is 0, so 1 and 1912 are divisors of 1912)
1912 / 2 = 956 (the remainder is 0, so 2 and 956 are divisors of 1912)
1912 / 3 = 637.33333333333 (the remainder is 1, so 3 is not a divisor of 1912)
...
1912 / 42 = 45.52380952381 (the remainder is 22, so 42 is not a divisor of 1912)
1912 / 43 = 44.46511627907 (the remainder is 20, so 43 is not a divisor of 1912)