What are the divisors of 4204?

1, 2, 4, 1051, 2102, 4204

There is a total of 6 positive divisors.
The sum of these divisors is 7364.
The arithmetic mean is 1227.3333333333.

4 even divisors

2, 4, 2102, 4204

2 odd divisors

1, 1051

How to compute the divisors of 4204?

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 4204 by each of the numbers from 1 to 4204 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)

4204 / 1 = 4204 (the remainder is 0, so 1 is a divisor of 4204)
4204 / 2 = 2102 (the remainder is 0, so 2 is a divisor of 4204)
4204 / 3 = 1401.3333333333 (the remainder is 1, so 3 is not a divisor of 4204)
...
4204 / 4203 = 1.0002379252915 (the remainder is 1, so 4203 is not a divisor of 4204)
4204 / 4204 = 1 (the remainder is 0, so 4204 is a divisor of 4204)

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 4204 (i.e. 64.838260309789). 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 $\frac{N}{d} = D$ )

4204 / 1 = 4204 (the remainder is 0, so 1 and 4204 are divisors of 4204)
4204 / 2 = 2102 (the remainder is 0, so 2 and 2102 are divisors of 4204)
4204 / 3 = 1401.3333333333 (the remainder is 1, so 3 is not a divisor of 4204)
...
4204 / 63 = 66.730158730159 (the remainder is 46, so 63 is not a divisor of 4204)
4204 / 64 = 65.6875 (the remainder is 44, so 64 is not a divisor of 4204)