What are the divisors of 606?

1, 2, 3, 6, 101, 202, 303, 606

There is a total of 8 positive divisors.
The sum of these divisors is 1224.
The arithmetic mean is 153.

4 even divisors

2, 6, 202, 606

4 odd divisors

1, 3, 101, 303

How to compute the divisors of 606?

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 606 by each of the numbers from 1 to 606 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)

606 / 1 = 606 (the remainder is 0, so 1 is a divisor of 606)
606 / 2 = 303 (the remainder is 0, so 2 is a divisor of 606)
606 / 3 = 202 (the remainder is 0, so 3 is a divisor of 606)
...
606 / 605 = 1.001652892562 (the remainder is 1, so 605 is not a divisor of 606)
606 / 606 = 1 (the remainder is 0, so 606 is a divisor of 606)

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 606 (i.e. 24.617067250182). 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 $\frac{N}{d} = D$ )

606 / 1 = 606 (the remainder is 0, so 1 and 606 are divisors of 606)
606 / 2 = 303 (the remainder is 0, so 2 and 303 are divisors of 606)
606 / 3 = 202 (the remainder is 0, so 3 and 202 are divisors of 606)
...
606 / 23 = 26.347826086957 (the remainder is 8, so 23 is not a divisor of 606)
606 / 24 = 25.25 (the remainder is 6, so 24 is not a divisor of 606)