What are the divisors of 702?

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

There is a total of 16 positive divisors.
The sum of these divisors is 1680.
The arithmetic mean is 105.

8 even divisors

2, 6, 18, 26, 54, 78, 234, 702

8 odd divisors

1, 3, 9, 13, 27, 39, 117, 351

How to compute the divisors of 702?

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 702 by each of the numbers from 1 to 702 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)

702 / 1 = 702 (the remainder is 0, so 1 is a divisor of 702)
702 / 2 = 351 (the remainder is 0, so 2 is a divisor of 702)
702 / 3 = 234 (the remainder is 0, so 3 is a divisor of 702)
...
702 / 701 = 1.0014265335235 (the remainder is 1, so 701 is not a divisor of 702)
702 / 702 = 1 (the remainder is 0, so 702 is a divisor of 702)

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 702 (i.e. 26.495282598984). 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 $\frac{N}{d} = D$ )

702 / 1 = 702 (the remainder is 0, so 1 and 702 are divisors of 702)
702 / 2 = 351 (the remainder is 0, so 2 and 351 are divisors of 702)
702 / 3 = 234 (the remainder is 0, so 3 and 234 are divisors of 702)
...
702 / 25 = 28.08 (the remainder is 2, so 25 is not a divisor of 702)
702 / 26 = 27 (the remainder is 0, so 26 and 27 are divisors of 702)