What are the divisors of 611?

1, 13, 47, 611

There is a total of 4 positive divisors.
The sum of these divisors is 672.
The arithmetic mean is 168.

4 odd divisors

1, 13, 47, 611

How to compute the divisors of 611?

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 611 by each of the numbers from 1 to 611 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)

611 / 1 = 611 (the remainder is 0, so 1 is a divisor of 611)
611 / 2 = 305.5 (the remainder is 1, so 2 is not a divisor of 611)
611 / 3 = 203.66666666667 (the remainder is 2, so 3 is not a divisor of 611)
...
611 / 610 = 1.0016393442623 (the remainder is 1, so 610 is not a divisor of 611)
611 / 611 = 1 (the remainder is 0, so 611 is a divisor of 611)

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 611 (i.e. 24.718414188617). 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 $\frac{N}{d} = D$ )

611 / 1 = 611 (the remainder is 0, so 1 and 611 are divisors of 611)
611 / 2 = 305.5 (the remainder is 1, so 2 is not a divisor of 611)
611 / 3 = 203.66666666667 (the remainder is 2, so 3 is not a divisor of 611)
...
611 / 23 = 26.565217391304 (the remainder is 13, so 23 is not a divisor of 611)
611 / 24 = 25.458333333333 (the remainder is 11, so 24 is not a divisor of 611)