What are the divisors of 4604?

1, 2, 4, 1151, 2302, 4604

There is a total of 6 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1344.

4 even divisors

2, 4, 2302, 4604

2 odd divisors

1, 1151

How to compute the divisors of 4604?

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 4604 by each of the numbers from 1 to 4604 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)

4604 / 1 = 4604 (the remainder is 0, so 1 is a divisor of 4604)
4604 / 2 = 2302 (the remainder is 0, so 2 is a divisor of 4604)
4604 / 3 = 1534.6666666667 (the remainder is 2, so 3 is not a divisor of 4604)
...
4604 / 4603 = 1.0002172496198 (the remainder is 1, so 4603 is not a divisor of 4604)
4604 / 4604 = 1 (the remainder is 0, so 4604 is a divisor of 4604)

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 4604 (i.e. 67.852781814749). 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 $\frac{N}{d} = D$ )

4604 / 1 = 4604 (the remainder is 0, so 1 and 4604 are divisors of 4604)
4604 / 2 = 2302 (the remainder is 0, so 2 and 2302 are divisors of 4604)
4604 / 3 = 1534.6666666667 (the remainder is 2, so 3 is not a divisor of 4604)
...
4604 / 66 = 69.757575757576 (the remainder is 50, so 66 is not a divisor of 4604)
4604 / 67 = 68.716417910448 (the remainder is 48, so 67 is not a divisor of 4604)