What are the divisors of 719?

1, 719

There is a total of 2 positive divisors.
The sum of these divisors is 720.
The arithmetic mean is 360.

2 odd divisors

1, 719

How to compute the divisors of 719?

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 719 by each of the numbers from 1 to 719 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)

719 / 1 = 719 (the remainder is 0, so 1 is a divisor of 719)
719 / 2 = 359.5 (the remainder is 1, so 2 is not a divisor of 719)
719 / 3 = 239.66666666667 (the remainder is 2, so 3 is not a divisor of 719)
...
719 / 718 = 1.0013927576602 (the remainder is 1, so 718 is not a divisor of 719)
719 / 719 = 1 (the remainder is 0, so 719 is a divisor of 719)

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 719 (i.e. 26.814175355584). 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 $\frac{N}{d} = D$ )

719 / 1 = 719 (the remainder is 0, so 1 and 719 are divisors of 719)
719 / 2 = 359.5 (the remainder is 1, so 2 is not a divisor of 719)
719 / 3 = 239.66666666667 (the remainder is 2, so 3 is not a divisor of 719)
...
719 / 25 = 28.76 (the remainder is 19, so 25 is not a divisor of 719)
719 / 26 = 27.653846153846 (the remainder is 17, so 26 is not a divisor of 719)