What are the divisors of 1924?

1, 2, 4, 13, 26, 37, 52, 74, 148, 481, 962, 1924

There is a total of 12 positive divisors.
The sum of these divisors is 3724.
The arithmetic mean is 310.33333333333.

8 even divisors

2, 4, 26, 52, 74, 148, 962, 1924

4 odd divisors

1, 13, 37, 481

How to compute the divisors of 1924?

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 1924 by each of the numbers from 1 to 1924 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)

1924 / 1 = 1924 (the remainder is 0, so 1 is a divisor of 1924)
1924 / 2 = 962 (the remainder is 0, so 2 is a divisor of 1924)
1924 / 3 = 641.33333333333 (the remainder is 1, so 3 is not a divisor of 1924)
...
1924 / 1923 = 1.0005200208008 (the remainder is 1, so 1923 is not a divisor of 1924)
1924 / 1924 = 1 (the remainder is 0, so 1924 is a divisor of 1924)

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 1924 (i.e. 43.863424398923). 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 $\frac{N}{d} = D$ )

1924 / 1 = 1924 (the remainder is 0, so 1 and 1924 are divisors of 1924)
1924 / 2 = 962 (the remainder is 0, so 2 and 962 are divisors of 1924)
1924 / 3 = 641.33333333333 (the remainder is 1, so 3 is not a divisor of 1924)
...
1924 / 42 = 45.809523809524 (the remainder is 34, so 42 is not a divisor of 1924)
1924 / 43 = 44.744186046512 (the remainder is 32, so 43 is not a divisor of 1924)