What are the divisors of 694?

1, 2, 347, 694

There is a total of 4 positive divisors.
The sum of these divisors is 1044.
The arithmetic mean is 261.

2 even divisors

2, 694

2 odd divisors

1, 347

How to compute the divisors of 694?

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 694 by each of the numbers from 1 to 694 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)

694 / 1 = 694 (the remainder is 0, so 1 is a divisor of 694)
694 / 2 = 347 (the remainder is 0, so 2 is a divisor of 694)
694 / 3 = 231.33333333333 (the remainder is 1, so 3 is not a divisor of 694)
...
694 / 693 = 1.001443001443 (the remainder is 1, so 693 is not a divisor of 694)
694 / 694 = 1 (the remainder is 0, so 694 is a divisor of 694)

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 694 (i.e. 26.343879744639). 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 $\frac{N}{d} = D$ )

694 / 1 = 694 (the remainder is 0, so 1 and 694 are divisors of 694)
694 / 2 = 347 (the remainder is 0, so 2 and 347 are divisors of 694)
694 / 3 = 231.33333333333 (the remainder is 1, so 3 is not a divisor of 694)
...
694 / 25 = 27.76 (the remainder is 19, so 25 is not a divisor of 694)
694 / 26 = 26.692307692308 (the remainder is 18, so 26 is not a divisor of 694)