What are the divisors of 3947?

1, 3947

There is a total of 2 positive divisors.
The sum of these divisors is 3948.
The arithmetic mean is 1974.

2 odd divisors

1, 3947

How to compute the divisors of 3947?

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 3947 by each of the numbers from 1 to 3947 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)

3947 / 1 = 3947 (the remainder is 0, so 1 is a divisor of 3947)
3947 / 2 = 1973.5 (the remainder is 1, so 2 is not a divisor of 3947)
3947 / 3 = 1315.6666666667 (the remainder is 2, so 3 is not a divisor of 3947)
...
3947 / 3946 = 1.000253421186 (the remainder is 1, so 3946 is not a divisor of 3947)
3947 / 3947 = 1 (the remainder is 0, so 3947 is a divisor of 3947)

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 3947 (i.e. 62.82515419798). 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 $\frac{N}{d} = D$ )

3947 / 1 = 3947 (the remainder is 0, so 1 and 3947 are divisors of 3947)
3947 / 2 = 1973.5 (the remainder is 1, so 2 is not a divisor of 3947)
3947 / 3 = 1315.6666666667 (the remainder is 2, so 3 is not a divisor of 3947)
...
3947 / 61 = 64.704918032787 (the remainder is 43, so 61 is not a divisor of 3947)
3947 / 62 = 63.661290322581 (the remainder is 41, so 62 is not a divisor of 3947)