What are the divisors of 4473?

1, 3, 7, 9, 21, 63, 71, 213, 497, 639, 1491, 4473

There is a total of 12 positive divisors.
The sum of these divisors is 7488.
The arithmetic mean is 624.

12 odd divisors

1, 3, 7, 9, 21, 63, 71, 213, 497, 639, 1491, 4473

How to compute the divisors of 4473?

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 4473 by each of the numbers from 1 to 4473 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)

4473 / 1 = 4473 (the remainder is 0, so 1 is a divisor of 4473)
4473 / 2 = 2236.5 (the remainder is 1, so 2 is not a divisor of 4473)
4473 / 3 = 1491 (the remainder is 0, so 3 is a divisor of 4473)
...
4473 / 4472 = 1.0002236135957 (the remainder is 1, so 4472 is not a divisor of 4473)
4473 / 4473 = 1 (the remainder is 0, so 4473 is a divisor of 4473)

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 4473 (i.e. 66.880490428824). 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 $\frac{N}{d} = D$ )

4473 / 1 = 4473 (the remainder is 0, so 1 and 4473 are divisors of 4473)
4473 / 2 = 2236.5 (the remainder is 1, so 2 is not a divisor of 4473)
4473 / 3 = 1491 (the remainder is 0, so 3 and 1491 are divisors of 4473)
...
4473 / 65 = 68.815384615385 (the remainder is 53, so 65 is not a divisor of 4473)
4473 / 66 = 67.772727272727 (the remainder is 51, so 66 is not a divisor of 4473)