What are the divisors of 4614?

1, 2, 3, 6, 769, 1538, 2307, 4614

There is a total of 8 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 1155.

4 even divisors

2, 6, 1538, 4614

4 odd divisors

1, 3, 769, 2307

How to compute the divisors of 4614?

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 4614 by each of the numbers from 1 to 4614 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)

4614 / 1 = 4614 (the remainder is 0, so 1 is a divisor of 4614)
4614 / 2 = 2307 (the remainder is 0, so 2 is a divisor of 4614)
4614 / 3 = 1538 (the remainder is 0, so 3 is a divisor of 4614)
...
4614 / 4613 = 1.000216778669 (the remainder is 1, so 4613 is not a divisor of 4614)
4614 / 4614 = 1 (the remainder is 0, so 4614 is a divisor of 4614)

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 4614 (i.e. 67.926430790967). 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 $\frac{N}{d} = D$ )

4614 / 1 = 4614 (the remainder is 0, so 1 and 4614 are divisors of 4614)
4614 / 2 = 2307 (the remainder is 0, so 2 and 2307 are divisors of 4614)
4614 / 3 = 1538 (the remainder is 0, so 3 and 1538 are divisors of 4614)
...
4614 / 66 = 69.909090909091 (the remainder is 60, so 66 is not a divisor of 4614)
4614 / 67 = 68.865671641791 (the remainder is 58, so 67 is not a divisor of 4614)