What are the divisors of 3890?

1, 2, 5, 10, 389, 778, 1945, 3890

There is a total of 8 positive divisors.
The sum of these divisors is 7020.
The arithmetic mean is 877.5.

4 even divisors

2, 10, 778, 3890

4 odd divisors

1, 5, 389, 1945

How to compute the divisors of 3890?

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 3890 by each of the numbers from 1 to 3890 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)

3890 / 1 = 3890 (the remainder is 0, so 1 is a divisor of 3890)
3890 / 2 = 1945 (the remainder is 0, so 2 is a divisor of 3890)
3890 / 3 = 1296.6666666667 (the remainder is 2, so 3 is not a divisor of 3890)
...
3890 / 3889 = 1.0002571355104 (the remainder is 1, so 3889 is not a divisor of 3890)
3890 / 3890 = 1 (the remainder is 0, so 3890 is a divisor of 3890)

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 3890 (i.e. 62.369864518051). 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 $\frac{N}{d} = D$ )

3890 / 1 = 3890 (the remainder is 0, so 1 and 3890 are divisors of 3890)
3890 / 2 = 1945 (the remainder is 0, so 2 and 1945 are divisors of 3890)
3890 / 3 = 1296.6666666667 (the remainder is 2, so 3 is not a divisor of 3890)
...
3890 / 61 = 63.770491803279 (the remainder is 47, so 61 is not a divisor of 3890)
3890 / 62 = 62.741935483871 (the remainder is 46, so 62 is not a divisor of 3890)