What are the divisors of 4658?

1, 2, 17, 34, 137, 274, 2329, 4658

There is a total of 8 positive divisors.
The sum of these divisors is 7452.
The arithmetic mean is 931.5.

4 even divisors

2, 34, 274, 4658

4 odd divisors

1, 17, 137, 2329

How to compute the divisors of 4658?

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 4658 by each of the numbers from 1 to 4658 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)

4658 / 1 = 4658 (the remainder is 0, so 1 is a divisor of 4658)
4658 / 2 = 2329 (the remainder is 0, so 2 is a divisor of 4658)
4658 / 3 = 1552.6666666667 (the remainder is 2, so 3 is not a divisor of 4658)
...
4658 / 4657 = 1.0002147305132 (the remainder is 1, so 4657 is not a divisor of 4658)
4658 / 4658 = 1 (the remainder is 0, so 4658 is a divisor of 4658)

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 4658 (i.e. 68.249542123006). 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 $\frac{N}{d} = D$ )

4658 / 1 = 4658 (the remainder is 0, so 1 and 4658 are divisors of 4658)
4658 / 2 = 2329 (the remainder is 0, so 2 and 2329 are divisors of 4658)
4658 / 3 = 1552.6666666667 (the remainder is 2, so 3 is not a divisor of 4658)
...
4658 / 67 = 69.522388059701 (the remainder is 35, so 67 is not a divisor of 4658)
4658 / 68 = 68.5 (the remainder is 34, so 68 is not a divisor of 4658)