What are the divisors of 4610?

1, 2, 5, 10, 461, 922, 2305, 4610

There is a total of 8 positive divisors.
The sum of these divisors is 8316.
The arithmetic mean is 1039.5.

4 even divisors

2, 10, 922, 4610

4 odd divisors

1, 5, 461, 2305

How to compute the divisors of 4610?

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 4610 by each of the numbers from 1 to 4610 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)

4610 / 1 = 4610 (the remainder is 0, so 1 is a divisor of 4610)
4610 / 2 = 2305 (the remainder is 0, so 2 is a divisor of 4610)
4610 / 3 = 1536.6666666667 (the remainder is 2, so 3 is not a divisor of 4610)
...
4610 / 4609 = 1.0002169668041 (the remainder is 1, so 4609 is not a divisor of 4610)
4610 / 4610 = 1 (the remainder is 0, so 4610 is a divisor of 4610)

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 4610 (i.e. 67.896980787072). 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 $\frac{N}{d} = D$ )

4610 / 1 = 4610 (the remainder is 0, so 1 and 4610 are divisors of 4610)
4610 / 2 = 2305 (the remainder is 0, so 2 and 2305 are divisors of 4610)
4610 / 3 = 1536.6666666667 (the remainder is 2, so 3 is not a divisor of 4610)
...
4610 / 66 = 69.848484848485 (the remainder is 56, so 66 is not a divisor of 4610)
4610 / 67 = 68.805970149254 (the remainder is 54, so 67 is not a divisor of 4610)