What are the divisors of 4373?

1, 4373

There is a total of 2 positive divisors.
The sum of these divisors is 4374.
The arithmetic mean is 2187.

2 odd divisors

1, 4373

How to compute the divisors of 4373?

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 4373 by each of the numbers from 1 to 4373 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)

4373 / 1 = 4373 (the remainder is 0, so 1 is a divisor of 4373)
4373 / 2 = 2186.5 (the remainder is 1, so 2 is not a divisor of 4373)
4373 / 3 = 1457.6666666667 (the remainder is 2, so 3 is not a divisor of 4373)
...
4373 / 4372 = 1.0002287282708 (the remainder is 1, so 4372 is not a divisor of 4373)
4373 / 4373 = 1 (the remainder is 0, so 4373 is a divisor of 4373)

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 4373 (i.e. 66.128662469462). 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 $\frac{N}{d} = D$ )

4373 / 1 = 4373 (the remainder is 0, so 1 and 4373 are divisors of 4373)
4373 / 2 = 2186.5 (the remainder is 1, so 2 is not a divisor of 4373)
4373 / 3 = 1457.6666666667 (the remainder is 2, so 3 is not a divisor of 4373)
...
4373 / 65 = 67.276923076923 (the remainder is 18, so 65 is not a divisor of 4373)
4373 / 66 = 66.257575757576 (the remainder is 17, so 66 is not a divisor of 4373)