What are the divisors of 603?

1, 3, 9, 67, 201, 603

There is a total of 6 positive divisors.
The sum of these divisors is 884.
The arithmetic mean is 147.33333333333.

6 odd divisors

1, 3, 9, 67, 201, 603

How to compute the divisors of 603?

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 603 by each of the numbers from 1 to 603 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)

603 / 1 = 603 (the remainder is 0, so 1 is a divisor of 603)
603 / 2 = 301.5 (the remainder is 1, so 2 is not a divisor of 603)
603 / 3 = 201 (the remainder is 0, so 3 is a divisor of 603)
...
603 / 602 = 1.0016611295681 (the remainder is 1, so 602 is not a divisor of 603)
603 / 603 = 1 (the remainder is 0, so 603 is a divisor of 603)

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 603 (i.e. 24.556058315617). 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 $\frac{N}{d} = D$ )

603 / 1 = 603 (the remainder is 0, so 1 and 603 are divisors of 603)
603 / 2 = 301.5 (the remainder is 1, so 2 is not a divisor of 603)
603 / 3 = 201 (the remainder is 0, so 3 and 201 are divisors of 603)
...
603 / 23 = 26.217391304348 (the remainder is 5, so 23 is not a divisor of 603)
603 / 24 = 25.125 (the remainder is 3, so 24 is not a divisor of 603)