What are the divisors of 4730?

1, 2, 5, 10, 11, 22, 43, 55, 86, 110, 215, 430, 473, 946, 2365, 4730

There is a total of 16 positive divisors.
The sum of these divisors is 9504.
The arithmetic mean is 594.

8 even divisors

2, 10, 22, 86, 110, 430, 946, 4730

8 odd divisors

1, 5, 11, 43, 55, 215, 473, 2365

How to compute the divisors of 4730?

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 4730 by each of the numbers from 1 to 4730 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)

4730 / 1 = 4730 (the remainder is 0, so 1 is a divisor of 4730)
4730 / 2 = 2365 (the remainder is 0, so 2 is a divisor of 4730)
4730 / 3 = 1576.6666666667 (the remainder is 2, so 3 is not a divisor of 4730)
...
4730 / 4729 = 1.0002114611969 (the remainder is 1, so 4729 is not a divisor of 4730)
4730 / 4730 = 1 (the remainder is 0, so 4730 is a divisor of 4730)

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 4730 (i.e. 68.774995456198). 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 $\frac{N}{d} = D$ )

4730 / 1 = 4730 (the remainder is 0, so 1 and 4730 are divisors of 4730)
4730 / 2 = 2365 (the remainder is 0, so 2 and 2365 are divisors of 4730)
4730 / 3 = 1576.6666666667 (the remainder is 2, so 3 is not a divisor of 4730)
...
4730 / 67 = 70.597014925373 (the remainder is 40, so 67 is not a divisor of 4730)
4730 / 68 = 69.558823529412 (the remainder is 38, so 68 is not a divisor of 4730)