What are the divisors of 4612?

1, 2, 4, 1153, 2306, 4612

There is a total of 6 positive divisors.
The sum of these divisors is 8078.
The arithmetic mean is 1346.3333333333.

4 even divisors

2, 4, 2306, 4612

2 odd divisors

1, 1153

How to compute the divisors of 4612?

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 4612 by each of the numbers from 1 to 4612 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)

4612 / 1 = 4612 (the remainder is 0, so 1 is a divisor of 4612)
4612 / 2 = 2306 (the remainder is 0, so 2 is a divisor of 4612)
4612 / 3 = 1537.3333333333 (the remainder is 1, so 3 is not a divisor of 4612)
...
4612 / 4611 = 1.0002168726957 (the remainder is 1, so 4611 is not a divisor of 4612)
4612 / 4612 = 1 (the remainder is 0, so 4612 is a divisor of 4612)

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 4612 (i.e. 67.911707385399). 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 $\frac{N}{d} = D$ )

4612 / 1 = 4612 (the remainder is 0, so 1 and 4612 are divisors of 4612)
4612 / 2 = 2306 (the remainder is 0, so 2 and 2306 are divisors of 4612)
4612 / 3 = 1537.3333333333 (the remainder is 1, so 3 is not a divisor of 4612)
...
4612 / 66 = 69.878787878788 (the remainder is 58, so 66 is not a divisor of 4612)
4612 / 67 = 68.835820895522 (the remainder is 56, so 67 is not a divisor of 4612)