What are the divisors of 673?

1, 673

There is a total of 2 positive divisors.
The sum of these divisors is 674.
The arithmetic mean is 337.

2 odd divisors

1, 673

How to compute the divisors of 673?

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 673 by each of the numbers from 1 to 673 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)

673 / 1 = 673 (the remainder is 0, so 1 is a divisor of 673)
673 / 2 = 336.5 (the remainder is 1, so 2 is not a divisor of 673)
673 / 3 = 224.33333333333 (the remainder is 1, so 3 is not a divisor of 673)
...
673 / 672 = 1.0014880952381 (the remainder is 1, so 672 is not a divisor of 673)
673 / 673 = 1 (the remainder is 0, so 673 is a divisor of 673)

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 673 (i.e. 25.942243542146). 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 $\frac{N}{d} = D$ )

673 / 1 = 673 (the remainder is 0, so 1 and 673 are divisors of 673)
673 / 2 = 336.5 (the remainder is 1, so 2 is not a divisor of 673)
673 / 3 = 224.33333333333 (the remainder is 1, so 3 is not a divisor of 673)
...
673 / 24 = 28.041666666667 (the remainder is 1, so 24 is not a divisor of 673)
673 / 25 = 26.92 (the remainder is 23, so 25 is not a divisor of 673)