What are the divisors of 3952?

1, 2, 4, 8, 13, 16, 19, 26, 38, 52, 76, 104, 152, 208, 247, 304, 494, 988, 1976, 3952

There is a total of 20 positive divisors.
The sum of these divisors is 8680.
The arithmetic mean is 434.

16 even divisors

2, 4, 8, 16, 26, 38, 52, 76, 104, 152, 208, 304, 494, 988, 1976, 3952

4 odd divisors

1, 13, 19, 247

How to compute the divisors of 3952?

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 3952 by each of the numbers from 1 to 3952 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)

3952 / 1 = 3952 (the remainder is 0, so 1 is a divisor of 3952)
3952 / 2 = 1976 (the remainder is 0, so 2 is a divisor of 3952)
3952 / 3 = 1317.3333333333 (the remainder is 1, so 3 is not a divisor of 3952)
...
3952 / 3951 = 1.0002531004809 (the remainder is 1, so 3951 is not a divisor of 3952)
3952 / 3952 = 1 (the remainder is 0, so 3952 is a divisor of 3952)

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 3952 (i.e. 62.864934582007). 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 $\frac{N}{d} = D$ )

3952 / 1 = 3952 (the remainder is 0, so 1 and 3952 are divisors of 3952)
3952 / 2 = 1976 (the remainder is 0, so 2 and 1976 are divisors of 3952)
3952 / 3 = 1317.3333333333 (the remainder is 1, so 3 is not a divisor of 3952)
...
3952 / 61 = 64.786885245902 (the remainder is 48, so 61 is not a divisor of 3952)
3952 / 62 = 63.741935483871 (the remainder is 46, so 62 is not a divisor of 3952)