What are the divisors of 700?

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

There is a total of 18 positive divisors.
The sum of these divisors is 1736.
The arithmetic mean is 96.444444444444.

12 even divisors

2, 4, 10, 14, 20, 28, 50, 70, 100, 140, 350, 700

6 odd divisors

1, 5, 7, 25, 35, 175

How to compute the divisors of 700?

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 700 by each of the numbers from 1 to 700 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)

700 / 1 = 700 (the remainder is 0, so 1 is a divisor of 700)
700 / 2 = 350 (the remainder is 0, so 2 is a divisor of 700)
700 / 3 = 233.33333333333 (the remainder is 1, so 3 is not a divisor of 700)
...
700 / 699 = 1.0014306151645 (the remainder is 1, so 699 is not a divisor of 700)
700 / 700 = 1 (the remainder is 0, so 700 is a divisor of 700)

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 700 (i.e. 26.457513110646). 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 $\frac{N}{d} = D$ )

700 / 1 = 700 (the remainder is 0, so 1 and 700 are divisors of 700)
700 / 2 = 350 (the remainder is 0, so 2 and 350 are divisors of 700)
700 / 3 = 233.33333333333 (the remainder is 1, so 3 is not a divisor of 700)
...
700 / 25 = 28 (the remainder is 0, so 25 and 28 are divisors of 700)
700 / 26 = 26.923076923077 (the remainder is 24, so 26 is not a divisor of 700)