What are the divisors of 4190?

1, 2, 5, 10, 419, 838, 2095, 4190

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

4 even divisors

2, 10, 838, 4190

4 odd divisors

1, 5, 419, 2095

How to compute the divisors of 4190?

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 4190 by each of the numbers from 1 to 4190 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)

4190 / 1 = 4190 (the remainder is 0, so 1 is a divisor of 4190)
4190 / 2 = 2095 (the remainder is 0, so 2 is a divisor of 4190)
4190 / 3 = 1396.6666666667 (the remainder is 2, so 3 is not a divisor of 4190)
...
4190 / 4189 = 1.0002387204583 (the remainder is 1, so 4189 is not a divisor of 4190)
4190 / 4190 = 1 (the remainder is 0, so 4190 is a divisor of 4190)

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 4190 (i.e. 64.730209330729). 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 $\frac{N}{d} = D$ )

4190 / 1 = 4190 (the remainder is 0, so 1 and 4190 are divisors of 4190)
4190 / 2 = 2095 (the remainder is 0, so 2 and 2095 are divisors of 4190)
4190 / 3 = 1396.6666666667 (the remainder is 2, so 3 is not a divisor of 4190)
...
4190 / 63 = 66.507936507937 (the remainder is 32, so 63 is not a divisor of 4190)
4190 / 64 = 65.46875 (the remainder is 30, so 64 is not a divisor of 4190)