What are the divisors of 695?

1, 5, 139, 695

There is a total of 4 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 210.

4 odd divisors

1, 5, 139, 695

How to compute the divisors of 695?

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 695 by each of the numbers from 1 to 695 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)

695 / 1 = 695 (the remainder is 0, so 1 is a divisor of 695)
695 / 2 = 347.5 (the remainder is 1, so 2 is not a divisor of 695)
695 / 3 = 231.66666666667 (the remainder is 2, so 3 is not a divisor of 695)
...
695 / 694 = 1.0014409221902 (the remainder is 1, so 694 is not a divisor of 695)
695 / 695 = 1 (the remainder is 0, so 695 is a divisor of 695)

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 695 (i.e. 26.362852652928). 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 $\frac{N}{d} = D$ )

695 / 1 = 695 (the remainder is 0, so 1 and 695 are divisors of 695)
695 / 2 = 347.5 (the remainder is 1, so 2 is not a divisor of 695)
695 / 3 = 231.66666666667 (the remainder is 2, so 3 is not a divisor of 695)
...
695 / 25 = 27.8 (the remainder is 20, so 25 is not a divisor of 695)
695 / 26 = 26.730769230769 (the remainder is 19, so 26 is not a divisor of 695)