What are the divisors of 3876?

1, 2, 3, 4, 6, 12, 17, 19, 34, 38, 51, 57, 68, 76, 102, 114, 204, 228, 323, 646, 969, 1292, 1938, 3876

There is a total of 24 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 420.

16 even divisors

2, 4, 6, 12, 34, 38, 68, 76, 102, 114, 204, 228, 646, 1292, 1938, 3876

8 odd divisors

1, 3, 17, 19, 51, 57, 323, 969

How to compute the divisors of 3876?

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 3876 by each of the numbers from 1 to 3876 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)

3876 / 1 = 3876 (the remainder is 0, so 1 is a divisor of 3876)
3876 / 2 = 1938 (the remainder is 0, so 2 is a divisor of 3876)
3876 / 3 = 1292 (the remainder is 0, so 3 is a divisor of 3876)
...
3876 / 3875 = 1.0002580645161 (the remainder is 1, so 3875 is not a divisor of 3876)
3876 / 3876 = 1 (the remainder is 0, so 3876 is a divisor of 3876)

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 3876 (i.e. 62.257529665094). 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 $\frac{N}{d} = D$ )

3876 / 1 = 3876 (the remainder is 0, so 1 and 3876 are divisors of 3876)
3876 / 2 = 1938 (the remainder is 0, so 2 and 1938 are divisors of 3876)
3876 / 3 = 1292 (the remainder is 0, so 3 and 1292 are divisors of 3876)
...
3876 / 61 = 63.540983606557 (the remainder is 33, so 61 is not a divisor of 3876)
3876 / 62 = 62.516129032258 (the remainder is 32, so 62 is not a divisor of 3876)