What are the divisors of 613?

1, 613

There is a total of 2 positive divisors.
The sum of these divisors is 614.
The arithmetic mean is 307.

2 odd divisors

1, 613

How to compute the divisors of 613?

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 613 by each of the numbers from 1 to 613 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)

613 / 1 = 613 (the remainder is 0, so 1 is a divisor of 613)
613 / 2 = 306.5 (the remainder is 1, so 2 is not a divisor of 613)
613 / 3 = 204.33333333333 (the remainder is 1, so 3 is not a divisor of 613)
...
613 / 612 = 1.0016339869281 (the remainder is 1, so 612 is not a divisor of 613)
613 / 613 = 1 (the remainder is 0, so 613 is a divisor of 613)

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 613 (i.e. 24.75883680628). 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 $\frac{N}{d} = D$ )

613 / 1 = 613 (the remainder is 0, so 1 and 613 are divisors of 613)
613 / 2 = 306.5 (the remainder is 1, so 2 is not a divisor of 613)
613 / 3 = 204.33333333333 (the remainder is 1, so 3 is not a divisor of 613)
...
613 / 23 = 26.652173913043 (the remainder is 15, so 23 is not a divisor of 613)
613 / 24 = 25.541666666667 (the remainder is 13, so 24 is not a divisor of 613)