What are the divisors of 182?

1, 2, 7, 13, 14, 26, 91, 182

There is a total of 8 positive divisors.
The sum of these divisors is 336.
The arithmetic mean is 42.

4 even divisors

2, 14, 26, 182

4 odd divisors

1, 7, 13, 91

How to compute the divisors of 182?

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 182 by each of the numbers from 1 to 182 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)

182 / 1 = 182 (the remainder is 0, so 1 is a divisor of 182)
182 / 2 = 91 (the remainder is 0, so 2 is a divisor of 182)
182 / 3 = 60.666666666667 (the remainder is 2, so 3 is not a divisor of 182)
...
182 / 181 = 1.0055248618785 (the remainder is 1, so 181 is not a divisor of 182)
182 / 182 = 1 (the remainder is 0, so 182 is a divisor of 182)

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 182 (i.e. 13.490737563232). 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 $\frac{N}{d} = D$ )

182 / 1 = 182 (the remainder is 0, so 1 and 182 are divisors of 182)
182 / 2 = 91 (the remainder is 0, so 2 and 91 are divisors of 182)
182 / 3 = 60.666666666667 (the remainder is 2, so 3 is not a divisor of 182)
...
182 / 12 = 15.166666666667 (the remainder is 2, so 12 is not a divisor of 182)
182 / 13 = 14 (the remainder is 0, so 13 and 14 are divisors of 182)