What are the divisors of 3872?

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 121, 176, 242, 352, 484, 968, 1936, 3872

There is a total of 18 positive divisors.
The sum of these divisors is 8379.
The arithmetic mean is 465.5.

15 even divisors

2, 4, 8, 16, 22, 32, 44, 88, 176, 242, 352, 484, 968, 1936, 3872

3 odd divisors

1, 11, 121

How to compute the divisors of 3872?

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 3872 by each of the numbers from 1 to 3872 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)

3872 / 1 = 3872 (the remainder is 0, so 1 is a divisor of 3872)
3872 / 2 = 1936 (the remainder is 0, so 2 is a divisor of 3872)
3872 / 3 = 1290.6666666667 (the remainder is 2, so 3 is not a divisor of 3872)
...
3872 / 3871 = 1.0002583311806 (the remainder is 1, so 3871 is not a divisor of 3872)
3872 / 3872 = 1 (the remainder is 0, so 3872 is a divisor of 3872)

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 3872 (i.e. 62.225396744416). 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 $\frac{N}{d} = D$ )

3872 / 1 = 3872 (the remainder is 0, so 1 and 3872 are divisors of 3872)
3872 / 2 = 1936 (the remainder is 0, so 2 and 1936 are divisors of 3872)
3872 / 3 = 1290.6666666667 (the remainder is 2, so 3 is not a divisor of 3872)
...
3872 / 61 = 63.475409836066 (the remainder is 29, so 61 is not a divisor of 3872)
3872 / 62 = 62.451612903226 (the remainder is 28, so 62 is not a divisor of 3872)