What are the divisors of 2702?

1, 2, 7, 14, 193, 386, 1351, 2702

There is a total of 8 positive divisors.
The sum of these divisors is 4656.
The arithmetic mean is 582.

4 even divisors

2, 14, 386, 2702

4 odd divisors

1, 7, 193, 1351

How to compute the divisors of 2702?

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 2702 by each of the numbers from 1 to 2702 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)

2702 / 1 = 2702 (the remainder is 0, so 1 is a divisor of 2702)
2702 / 2 = 1351 (the remainder is 0, so 2 is a divisor of 2702)
2702 / 3 = 900.66666666667 (the remainder is 2, so 3 is not a divisor of 2702)
...
2702 / 2701 = 1.0003702332469 (the remainder is 1, so 2701 is not a divisor of 2702)
2702 / 2702 = 1 (the remainder is 0, so 2702 is a divisor of 2702)

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 2702 (i.e. 51.980765673468). 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 $\frac{N}{d} = D$ )

2702 / 1 = 2702 (the remainder is 0, so 1 and 2702 are divisors of 2702)
2702 / 2 = 1351 (the remainder is 0, so 2 and 1351 are divisors of 2702)
2702 / 3 = 900.66666666667 (the remainder is 2, so 3 is not a divisor of 2702)
...
2702 / 50 = 54.04 (the remainder is 2, so 50 is not a divisor of 2702)
2702 / 51 = 52.980392156863 (the remainder is 50, so 51 is not a divisor of 2702)