What are the divisors of 3946?

1, 2, 1973, 3946

There is a total of 4 positive divisors.
The sum of these divisors is 5922.
The arithmetic mean is 1480.5.

2 even divisors

2, 3946

2 odd divisors

1, 1973

How to compute the divisors of 3946?

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 3946 by each of the numbers from 1 to 3946 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)

3946 / 1 = 3946 (the remainder is 0, so 1 is a divisor of 3946)
3946 / 2 = 1973 (the remainder is 0, so 2 is a divisor of 3946)
3946 / 3 = 1315.3333333333 (the remainder is 1, so 3 is not a divisor of 3946)
...
3946 / 3945 = 1.0002534854246 (the remainder is 1, so 3945 is not a divisor of 3946)
3946 / 3946 = 1 (the remainder is 0, so 3946 is a divisor of 3946)

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 3946 (i.e. 62.817195098158). 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 $\frac{N}{d} = D$ )

3946 / 1 = 3946 (the remainder is 0, so 1 and 3946 are divisors of 3946)
3946 / 2 = 1973 (the remainder is 0, so 2 and 1973 are divisors of 3946)
3946 / 3 = 1315.3333333333 (the remainder is 1, so 3 is not a divisor of 3946)
...
3946 / 61 = 64.688524590164 (the remainder is 42, so 61 is not a divisor of 3946)
3946 / 62 = 63.645161290323 (the remainder is 40, so 62 is not a divisor of 3946)