What are the divisors of 3976?

1, 2, 4, 7, 8, 14, 28, 56, 71, 142, 284, 497, 568, 994, 1988, 3976

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

12 even divisors

2, 4, 8, 14, 28, 56, 142, 284, 568, 994, 1988, 3976

4 odd divisors

1, 7, 71, 497

How to compute the divisors of 3976?

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 3976 by each of the numbers from 1 to 3976 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)

3976 / 1 = 3976 (the remainder is 0, so 1 is a divisor of 3976)
3976 / 2 = 1988 (the remainder is 0, so 2 is a divisor of 3976)
3976 / 3 = 1325.3333333333 (the remainder is 1, so 3 is not a divisor of 3976)
...
3976 / 3975 = 1.000251572327 (the remainder is 1, so 3975 is not a divisor of 3976)
3976 / 3976 = 1 (the remainder is 0, so 3976 is a divisor of 3976)

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 3976 (i.e. 63.055531081738). 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 $\frac{N}{d} = D$ )

3976 / 1 = 3976 (the remainder is 0, so 1 and 3976 are divisors of 3976)
3976 / 2 = 1988 (the remainder is 0, so 2 and 1988 are divisors of 3976)
3976 / 3 = 1325.3333333333 (the remainder is 1, so 3 is not a divisor of 3976)
...
3976 / 62 = 64.129032258065 (the remainder is 8, so 62 is not a divisor of 3976)
3976 / 63 = 63.111111111111 (the remainder is 7, so 63 is not a divisor of 3976)