What are the divisors of 4124?

1, 2, 4, 1031, 2062, 4124

There is a total of 6 positive divisors.
The sum of these divisors is 7224.
The arithmetic mean is 1204.

4 even divisors

2, 4, 2062, 4124

2 odd divisors

1, 1031

How to compute the divisors of 4124?

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 4124 by each of the numbers from 1 to 4124 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)

4124 / 1 = 4124 (the remainder is 0, so 1 is a divisor of 4124)
4124 / 2 = 2062 (the remainder is 0, so 2 is a divisor of 4124)
4124 / 3 = 1374.6666666667 (the remainder is 2, so 3 is not a divisor of 4124)
...
4124 / 4123 = 1.0002425418385 (the remainder is 1, so 4123 is not a divisor of 4124)
4124 / 4124 = 1 (the remainder is 0, so 4124 is a divisor of 4124)

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 4124 (i.e. 64.218377432009). 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 $\frac{N}{d} = D$ )

4124 / 1 = 4124 (the remainder is 0, so 1 and 4124 are divisors of 4124)
4124 / 2 = 2062 (the remainder is 0, so 2 and 2062 are divisors of 4124)
4124 / 3 = 1374.6666666667 (the remainder is 2, so 3 is not a divisor of 4124)
...
4124 / 63 = 65.460317460317 (the remainder is 29, so 63 is not a divisor of 4124)
4124 / 64 = 64.4375 (the remainder is 28, so 64 is not a divisor of 4124)