What are the divisors of 3932?

1, 2, 4, 983, 1966, 3932

There is a total of 6 positive divisors.
The sum of these divisors is 6888.
The arithmetic mean is 1148.

4 even divisors

2, 4, 1966, 3932

2 odd divisors

1, 983

How to compute the divisors of 3932?

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 3932 by each of the numbers from 1 to 3932 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)

3932 / 1 = 3932 (the remainder is 0, so 1 is a divisor of 3932)
3932 / 2 = 1966 (the remainder is 0, so 2 is a divisor of 3932)
3932 / 3 = 1310.6666666667 (the remainder is 2, so 3 is not a divisor of 3932)
...
3932 / 3931 = 1.0002543881964 (the remainder is 1, so 3931 is not a divisor of 3932)
3932 / 3932 = 1 (the remainder is 0, so 3932 is a divisor of 3932)

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 3932 (i.e. 62.705661626364). 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 $\frac{N}{d} = D$ )

3932 / 1 = 3932 (the remainder is 0, so 1 and 3932 are divisors of 3932)
3932 / 2 = 1966 (the remainder is 0, so 2 and 1966 are divisors of 3932)
3932 / 3 = 1310.6666666667 (the remainder is 2, so 3 is not a divisor of 3932)
...
3932 / 61 = 64.459016393443 (the remainder is 28, so 61 is not a divisor of 3932)
3932 / 62 = 63.41935483871 (the remainder is 26, so 62 is not a divisor of 3932)