What are the divisors of 739?

1, 739

There is a total of 2 positive divisors.
The sum of these divisors is 740.
The arithmetic mean is 370.

2 odd divisors

1, 739

How to compute the divisors of 739?

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 739 by each of the numbers from 1 to 739 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)

739 / 1 = 739 (the remainder is 0, so 1 is a divisor of 739)
739 / 2 = 369.5 (the remainder is 1, so 2 is not a divisor of 739)
739 / 3 = 246.33333333333 (the remainder is 1, so 3 is not a divisor of 739)
...
739 / 738 = 1.0013550135501 (the remainder is 1, so 738 is not a divisor of 739)
739 / 739 = 1 (the remainder is 0, so 739 is a divisor of 739)

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 739 (i.e. 27.184554438136). 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 $\frac{N}{d} = D$ )

739 / 1 = 739 (the remainder is 0, so 1 and 739 are divisors of 739)
739 / 2 = 369.5 (the remainder is 1, so 2 is not a divisor of 739)
739 / 3 = 246.33333333333 (the remainder is 1, so 3 is not a divisor of 739)
...
739 / 26 = 28.423076923077 (the remainder is 11, so 26 is not a divisor of 739)
739 / 27 = 27.37037037037 (the remainder is 10, so 27 is not a divisor of 739)