What are the divisors of 3848?

1, 2, 4, 8, 13, 26, 37, 52, 74, 104, 148, 296, 481, 962, 1924, 3848

There is a total of 16 positive divisors.
The sum of these divisors is 7980.
The arithmetic mean is 498.75.

12 even divisors

2, 4, 8, 26, 52, 74, 104, 148, 296, 962, 1924, 3848

4 odd divisors

1, 13, 37, 481

How to compute the divisors of 3848?

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 3848 by each of the numbers from 1 to 3848 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)

3848 / 1 = 3848 (the remainder is 0, so 1 is a divisor of 3848)
3848 / 2 = 1924 (the remainder is 0, so 2 is a divisor of 3848)
3848 / 3 = 1282.6666666667 (the remainder is 2, so 3 is not a divisor of 3848)
...
3848 / 3847 = 1.0002599428126 (the remainder is 1, so 3847 is not a divisor of 3848)
3848 / 3848 = 1 (the remainder is 0, so 3848 is a divisor of 3848)

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 3848 (i.e. 62.032249677083). 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 $\frac{N}{d} = D$ )

3848 / 1 = 3848 (the remainder is 0, so 1 and 3848 are divisors of 3848)
3848 / 2 = 1924 (the remainder is 0, so 2 and 1924 are divisors of 3848)
3848 / 3 = 1282.6666666667 (the remainder is 2, so 3 is not a divisor of 3848)
...
3848 / 61 = 63.081967213115 (the remainder is 5, so 61 is not a divisor of 3848)
3848 / 62 = 62.064516129032 (the remainder is 4, so 62 is not a divisor of 3848)