What are the divisors of 4673?

1, 4673

There is a total of 2 positive divisors.
The sum of these divisors is 4674.
The arithmetic mean is 2337.

2 odd divisors

1, 4673

How to compute the divisors of 4673?

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 4673 by each of the numbers from 1 to 4673 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)

4673 / 1 = 4673 (the remainder is 0, so 1 is a divisor of 4673)
4673 / 2 = 2336.5 (the remainder is 1, so 2 is not a divisor of 4673)
4673 / 3 = 1557.6666666667 (the remainder is 2, so 3 is not a divisor of 4673)
...
4673 / 4672 = 1.0002140410959 (the remainder is 1, so 4672 is not a divisor of 4673)
4673 / 4673 = 1 (the remainder is 0, so 4673 is a divisor of 4673)

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 4673 (i.e. 68.35934464285). 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 $\frac{N}{d} = D$ )

4673 / 1 = 4673 (the remainder is 0, so 1 and 4673 are divisors of 4673)
4673 / 2 = 2336.5 (the remainder is 1, so 2 is not a divisor of 4673)
4673 / 3 = 1557.6666666667 (the remainder is 2, so 3 is not a divisor of 4673)
...
4673 / 67 = 69.746268656716 (the remainder is 50, so 67 is not a divisor of 4673)
4673 / 68 = 68.720588235294 (the remainder is 49, so 68 is not a divisor of 4673)