What are the divisors of 671?

1, 11, 61, 671

There is a total of 4 positive divisors.
The sum of these divisors is 744.
The arithmetic mean is 186.

4 odd divisors

1, 11, 61, 671

How to compute the divisors of 671?

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 671 by each of the numbers from 1 to 671 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)

671 / 1 = 671 (the remainder is 0, so 1 is a divisor of 671)
671 / 2 = 335.5 (the remainder is 1, so 2 is not a divisor of 671)
671 / 3 = 223.66666666667 (the remainder is 2, so 3 is not a divisor of 671)
...
671 / 670 = 1.0014925373134 (the remainder is 1, so 670 is not a divisor of 671)
671 / 671 = 1 (the remainder is 0, so 671 is a divisor of 671)

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 671 (i.e. 25.903667693977). 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 $\frac{N}{d} = D$ )

671 / 1 = 671 (the remainder is 0, so 1 and 671 are divisors of 671)
671 / 2 = 335.5 (the remainder is 1, so 2 is not a divisor of 671)
671 / 3 = 223.66666666667 (the remainder is 2, so 3 is not a divisor of 671)
...
671 / 24 = 27.958333333333 (the remainder is 23, so 24 is not a divisor of 671)
671 / 25 = 26.84 (the remainder is 21, so 25 is not a divisor of 671)