What are the divisors of 4184?

1, 2, 4, 8, 523, 1046, 2092, 4184

There is a total of 8 positive divisors.
The sum of these divisors is 7860.
The arithmetic mean is 982.5.

6 even divisors

2, 4, 8, 1046, 2092, 4184

2 odd divisors

1, 523

How to compute the divisors of 4184?

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 4184 by each of the numbers from 1 to 4184 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)

4184 / 1 = 4184 (the remainder is 0, so 1 is a divisor of 4184)
4184 / 2 = 2092 (the remainder is 0, so 2 is a divisor of 4184)
4184 / 3 = 1394.6666666667 (the remainder is 2, so 3 is not a divisor of 4184)
...
4184 / 4183 = 1.0002390628735 (the remainder is 1, so 4183 is not a divisor of 4184)
4184 / 4184 = 1 (the remainder is 0, so 4184 is a divisor of 4184)

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 4184 (i.e. 64.683846515185). 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 $\frac{N}{d} = D$ )

4184 / 1 = 4184 (the remainder is 0, so 1 and 4184 are divisors of 4184)
4184 / 2 = 2092 (the remainder is 0, so 2 and 2092 are divisors of 4184)
4184 / 3 = 1394.6666666667 (the remainder is 2, so 3 is not a divisor of 4184)
...
4184 / 63 = 66.412698412698 (the remainder is 26, so 63 is not a divisor of 4184)
4184 / 64 = 65.375 (the remainder is 24, so 64 is not a divisor of 4184)