What are the divisors of 4600?

1, 2, 4, 5, 8, 10, 20, 23, 25, 40, 46, 50, 92, 100, 115, 184, 200, 230, 460, 575, 920, 1150, 2300, 4600

There is a total of 24 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 465.

18 even divisors

2, 4, 8, 10, 20, 40, 46, 50, 92, 100, 184, 200, 230, 460, 920, 1150, 2300, 4600

6 odd divisors

1, 5, 23, 25, 115, 575

How to compute the divisors of 4600?

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 4600 by each of the numbers from 1 to 4600 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)

4600 / 1 = 4600 (the remainder is 0, so 1 is a divisor of 4600)
4600 / 2 = 2300 (the remainder is 0, so 2 is a divisor of 4600)
4600 / 3 = 1533.3333333333 (the remainder is 1, so 3 is not a divisor of 4600)
...
4600 / 4599 = 1.0002174385736 (the remainder is 1, so 4599 is not a divisor of 4600)
4600 / 4600 = 1 (the remainder is 0, so 4600 is a divisor of 4600)

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 4600 (i.e. 67.823299831253). 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 $\frac{N}{d} = D$ )

4600 / 1 = 4600 (the remainder is 0, so 1 and 4600 are divisors of 4600)
4600 / 2 = 2300 (the remainder is 0, so 2 and 2300 are divisors of 4600)
4600 / 3 = 1533.3333333333 (the remainder is 1, so 3 is not a divisor of 4600)
...
4600 / 66 = 69.69696969697 (the remainder is 46, so 66 is not a divisor of 4600)
4600 / 67 = 68.65671641791 (the remainder is 44, so 67 is not a divisor of 4600)