What are the divisors of 605?

1, 5, 11, 55, 121, 605

There is a total of 6 positive divisors.
The sum of these divisors is 798.
The arithmetic mean is 133.

6 odd divisors

1, 5, 11, 55, 121, 605

How to compute the divisors of 605?

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 605 by each of the numbers from 1 to 605 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)

605 / 1 = 605 (the remainder is 0, so 1 is a divisor of 605)
605 / 2 = 302.5 (the remainder is 1, so 2 is not a divisor of 605)
605 / 3 = 201.66666666667 (the remainder is 2, so 3 is not a divisor of 605)
...
605 / 604 = 1.0016556291391 (the remainder is 1, so 604 is not a divisor of 605)
605 / 605 = 1 (the remainder is 0, so 605 is a divisor of 605)

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 605 (i.e. 24.596747752498). 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 $\frac{N}{d} = D$ )

605 / 1 = 605 (the remainder is 0, so 1 and 605 are divisors of 605)
605 / 2 = 302.5 (the remainder is 1, so 2 is not a divisor of 605)
605 / 3 = 201.66666666667 (the remainder is 2, so 3 is not a divisor of 605)
...
605 / 23 = 26.304347826087 (the remainder is 7, so 23 is not a divisor of 605)
605 / 24 = 25.208333333333 (the remainder is 5, so 24 is not a divisor of 605)