What are the divisors of 707?

1, 7, 101, 707

There is a total of 4 positive divisors.
The sum of these divisors is 816.
The arithmetic mean is 204.

4 odd divisors

1, 7, 101, 707

How to compute the divisors of 707?

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 707 by each of the numbers from 1 to 707 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)

707 / 1 = 707 (the remainder is 0, so 1 is a divisor of 707)
707 / 2 = 353.5 (the remainder is 1, so 2 is not a divisor of 707)
707 / 3 = 235.66666666667 (the remainder is 2, so 3 is not a divisor of 707)
...
707 / 706 = 1.0014164305949 (the remainder is 1, so 706 is not a divisor of 707)
707 / 707 = 1 (the remainder is 0, so 707 is a divisor of 707)

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 707 (i.e. 26.589471600617). 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 $\frac{N}{d} = D$ )

707 / 1 = 707 (the remainder is 0, so 1 and 707 are divisors of 707)
707 / 2 = 353.5 (the remainder is 1, so 2 is not a divisor of 707)
707 / 3 = 235.66666666667 (the remainder is 2, so 3 is not a divisor of 707)
...
707 / 25 = 28.28 (the remainder is 7, so 25 is not a divisor of 707)
707 / 26 = 27.192307692308 (the remainder is 5, so 26 is not a divisor of 707)