What are the divisors of 3852?

1, 2, 3, 4, 6, 9, 12, 18, 36, 107, 214, 321, 428, 642, 963, 1284, 1926, 3852

There is a total of 18 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 546.

12 even divisors

2, 4, 6, 12, 18, 36, 214, 428, 642, 1284, 1926, 3852

6 odd divisors

1, 3, 9, 107, 321, 963

How to compute the divisors of 3852?

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 3852 by each of the numbers from 1 to 3852 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)

3852 / 1 = 3852 (the remainder is 0, so 1 is a divisor of 3852)
3852 / 2 = 1926 (the remainder is 0, so 2 is a divisor of 3852)
3852 / 3 = 1284 (the remainder is 0, so 3 is a divisor of 3852)
...
3852 / 3851 = 1.0002596728123 (the remainder is 1, so 3851 is not a divisor of 3852)
3852 / 3852 = 1 (the remainder is 0, so 3852 is a divisor of 3852)

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 3852 (i.e. 62.064482596732). 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 $\frac{N}{d} = D$ )

3852 / 1 = 3852 (the remainder is 0, so 1 and 3852 are divisors of 3852)
3852 / 2 = 1926 (the remainder is 0, so 2 and 1926 are divisors of 3852)
3852 / 3 = 1284 (the remainder is 0, so 3 and 1284 are divisors of 3852)
...
3852 / 61 = 63.147540983607 (the remainder is 9, so 61 is not a divisor of 3852)
3852 / 62 = 62.129032258065 (the remainder is 8, so 62 is not a divisor of 3852)