What are the divisors of 3930?

1, 2, 3, 5, 6, 10, 15, 30, 131, 262, 393, 655, 786, 1310, 1965, 3930

There is a total of 16 positive divisors.
The sum of these divisors is 9504.
The arithmetic mean is 594.

8 even divisors

2, 6, 10, 30, 262, 786, 1310, 3930

8 odd divisors

1, 3, 5, 15, 131, 393, 655, 1965

How to compute the divisors of 3930?

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 3930 by each of the numbers from 1 to 3930 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)

3930 / 1 = 3930 (the remainder is 0, so 1 is a divisor of 3930)
3930 / 2 = 1965 (the remainder is 0, so 2 is a divisor of 3930)
3930 / 3 = 1310 (the remainder is 0, so 3 is a divisor of 3930)
...
3930 / 3929 = 1.000254517689 (the remainder is 1, so 3929 is not a divisor of 3930)
3930 / 3930 = 1 (the remainder is 0, so 3930 is a divisor of 3930)

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 3930 (i.e. 62.68971207463). 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 $\frac{N}{d} = D$ )

3930 / 1 = 3930 (the remainder is 0, so 1 and 3930 are divisors of 3930)
3930 / 2 = 1965 (the remainder is 0, so 2 and 1965 are divisors of 3930)
3930 / 3 = 1310 (the remainder is 0, so 3 and 1310 are divisors of 3930)
...
3930 / 61 = 64.426229508197 (the remainder is 26, so 61 is not a divisor of 3930)
3930 / 62 = 63.387096774194 (the remainder is 24, so 62 is not a divisor of 3930)