What are the divisors of 704?

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704

There is a total of 14 positive divisors.
The sum of these divisors is 1524.
The arithmetic mean is 108.85714285714.

12 even divisors

2, 4, 8, 16, 22, 32, 44, 64, 88, 176, 352, 704

2 odd divisors

1, 11

How to compute the divisors of 704?

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 704 by each of the numbers from 1 to 704 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)

704 / 1 = 704 (the remainder is 0, so 1 is a divisor of 704)
704 / 2 = 352 (the remainder is 0, so 2 is a divisor of 704)
704 / 3 = 234.66666666667 (the remainder is 2, so 3 is not a divisor of 704)
...
704 / 703 = 1.0014224751067 (the remainder is 1, so 703 is not a divisor of 704)
704 / 704 = 1 (the remainder is 0, so 704 is a divisor of 704)

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 704 (i.e. 26.532998322843). 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 $\frac{N}{d} = D$ )

704 / 1 = 704 (the remainder is 0, so 1 and 704 are divisors of 704)
704 / 2 = 352 (the remainder is 0, so 2 and 352 are divisors of 704)
704 / 3 = 234.66666666667 (the remainder is 2, so 3 is not a divisor of 704)
...
704 / 25 = 28.16 (the remainder is 4, so 25 is not a divisor of 704)
704 / 26 = 27.076923076923 (the remainder is 2, so 26 is not a divisor of 704)