What are the divisors of 734?

1, 2, 367, 734

There is a total of 4 positive divisors.
The sum of these divisors is 1104.
The arithmetic mean is 276.

2 even divisors

2, 734

2 odd divisors

1, 367

How to compute the divisors of 734?

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 734 by each of the numbers from 1 to 734 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)

734 / 1 = 734 (the remainder is 0, so 1 is a divisor of 734)
734 / 2 = 367 (the remainder is 0, so 2 is a divisor of 734)
734 / 3 = 244.66666666667 (the remainder is 2, so 3 is not a divisor of 734)
...
734 / 733 = 1.0013642564802 (the remainder is 1, so 733 is not a divisor of 734)
734 / 734 = 1 (the remainder is 0, so 734 is a divisor of 734)

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 734 (i.e. 27.092434368288). 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 $\frac{N}{d} = D$ )

734 / 1 = 734 (the remainder is 0, so 1 and 734 are divisors of 734)
734 / 2 = 367 (the remainder is 0, so 2 and 367 are divisors of 734)
734 / 3 = 244.66666666667 (the remainder is 2, so 3 is not a divisor of 734)
...
734 / 26 = 28.230769230769 (the remainder is 6, so 26 is not a divisor of 734)
734 / 27 = 27.185185185185 (the remainder is 5, so 27 is not a divisor of 734)