What are the divisors of 1936?

1, 2, 4, 8, 11, 16, 22, 44, 88, 121, 176, 242, 484, 968, 1936

There is a total of 15 positive divisors.
The sum of these divisors is 4123.
The arithmetic mean is 274.86666666667.

12 even divisors

2, 4, 8, 16, 22, 44, 88, 176, 242, 484, 968, 1936

3 odd divisors

1, 11, 121

How to compute the divisors of 1936?

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 1936 by each of the numbers from 1 to 1936 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)

1936 / 1 = 1936 (the remainder is 0, so 1 is a divisor of 1936)
1936 / 2 = 968 (the remainder is 0, so 2 is a divisor of 1936)
1936 / 3 = 645.33333333333 (the remainder is 1, so 3 is not a divisor of 1936)
...
1936 / 1935 = 1.0005167958656 (the remainder is 1, so 1935 is not a divisor of 1936)
1936 / 1936 = 1 (the remainder is 0, so 1936 is a divisor of 1936)

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 1936 (i.e. 44). 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 $\frac{N}{d} = D$ )

1936 / 1 = 1936 (the remainder is 0, so 1 and 1936 are divisors of 1936)
1936 / 2 = 968 (the remainder is 0, so 2 and 968 are divisors of 1936)
1936 / 3 = 645.33333333333 (the remainder is 1, so 3 is not a divisor of 1936)
...
1936 / 43 = 45.023255813953 (the remainder is 1, so 43 is not a divisor of 1936)
1936 / 44 = 44 (the remainder is 0, so 44 and 44 are divisors of 1936)