What are the divisors of 3860?

1, 2, 4, 5, 10, 20, 193, 386, 772, 965, 1930, 3860

There is a total of 12 positive divisors.
The sum of these divisors is 8148.
The arithmetic mean is 679.

8 even divisors

2, 4, 10, 20, 386, 772, 1930, 3860

4 odd divisors

1, 5, 193, 965

How to compute the divisors of 3860?

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 3860 by each of the numbers from 1 to 3860 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)

3860 / 1 = 3860 (the remainder is 0, so 1 is a divisor of 3860)
3860 / 2 = 1930 (the remainder is 0, so 2 is a divisor of 3860)
3860 / 3 = 1286.6666666667 (the remainder is 2, so 3 is not a divisor of 3860)
...
3860 / 3859 = 1.0002591344908 (the remainder is 1, so 3859 is not a divisor of 3860)
3860 / 3860 = 1 (the remainder is 0, so 3860 is a divisor of 3860)

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 3860 (i.e. 62.128898268036). 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 $\frac{N}{d} = D$ )

3860 / 1 = 3860 (the remainder is 0, so 1 and 3860 are divisors of 3860)
3860 / 2 = 1930 (the remainder is 0, so 2 and 1930 are divisors of 3860)
3860 / 3 = 1286.6666666667 (the remainder is 2, so 3 is not a divisor of 3860)
...
3860 / 61 = 63.27868852459 (the remainder is 17, so 61 is not a divisor of 3860)
3860 / 62 = 62.258064516129 (the remainder is 16, so 62 is not a divisor of 3860)