What are the divisors of 1473?

1, 3, 491, 1473

There is a total of 4 positive divisors.
The sum of these divisors is 1968.
The arithmetic mean is 492.

4 odd divisors

1, 3, 491, 1473

How to compute the divisors of 1473?

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 1473 by each of the numbers from 1 to 1473 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)

1473 / 1 = 1473 (the remainder is 0, so 1 is a divisor of 1473)
1473 / 2 = 736.5 (the remainder is 1, so 2 is not a divisor of 1473)
1473 / 3 = 491 (the remainder is 0, so 3 is a divisor of 1473)
...
1473 / 1472 = 1.0006793478261 (the remainder is 1, so 1472 is not a divisor of 1473)
1473 / 1473 = 1 (the remainder is 0, so 1473 is a divisor of 1473)

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 1473 (i.e. 38.379682124791). 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 $\frac{N}{d} = D$ )

1473 / 1 = 1473 (the remainder is 0, so 1 and 1473 are divisors of 1473)
1473 / 2 = 736.5 (the remainder is 1, so 2 is not a divisor of 1473)
1473 / 3 = 491 (the remainder is 0, so 3 and 491 are divisors of 1473)
...
1473 / 37 = 39.810810810811 (the remainder is 30, so 37 is not a divisor of 1473)
1473 / 38 = 38.763157894737 (the remainder is 29, so 38 is not a divisor of 1473)