What are the divisors of 710?

1, 2, 5, 10, 71, 142, 355, 710

There is a total of 8 positive divisors.
The sum of these divisors is 1296.
The arithmetic mean is 162.

4 even divisors

2, 10, 142, 710

4 odd divisors

1, 5, 71, 355

How to compute the divisors of 710?

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 710 by each of the numbers from 1 to 710 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)

710 / 1 = 710 (the remainder is 0, so 1 is a divisor of 710)
710 / 2 = 355 (the remainder is 0, so 2 is a divisor of 710)
710 / 3 = 236.66666666667 (the remainder is 2, so 3 is not a divisor of 710)
...
710 / 709 = 1.0014104372355 (the remainder is 1, so 709 is not a divisor of 710)
710 / 710 = 1 (the remainder is 0, so 710 is a divisor of 710)

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 710 (i.e. 26.645825188948). 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 $\frac{N}{d} = D$ )

710 / 1 = 710 (the remainder is 0, so 1 and 710 are divisors of 710)
710 / 2 = 355 (the remainder is 0, so 2 and 355 are divisors of 710)
710 / 3 = 236.66666666667 (the remainder is 2, so 3 is not a divisor of 710)
...
710 / 25 = 28.4 (the remainder is 10, so 25 is not a divisor of 710)
710 / 26 = 27.307692307692 (the remainder is 8, so 26 is not a divisor of 710)