What are the divisors of 136?

1, 2, 4, 8, 17, 34, 68, 136

There is a total of 8 positive divisors.
The sum of these divisors is 270.
The arithmetic mean is 33.75.

6 even divisors

2, 4, 8, 34, 68, 136

2 odd divisors

1, 17

How to compute the divisors of 136?

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 136 by each of the numbers from 1 to 136 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)

136 / 1 = 136 (the remainder is 0, so 1 is a divisor of 136)
136 / 2 = 68 (the remainder is 0, so 2 is a divisor of 136)
136 / 3 = 45.333333333333 (the remainder is 1, so 3 is not a divisor of 136)
...
136 / 135 = 1.0074074074074 (the remainder is 1, so 135 is not a divisor of 136)
136 / 136 = 1 (the remainder is 0, so 136 is a divisor of 136)

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 136 (i.e. 11.661903789691). 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 $\frac{N}{d} = D$ )

136 / 1 = 136 (the remainder is 0, so 1 and 136 are divisors of 136)
136 / 2 = 68 (the remainder is 0, so 2 and 68 are divisors of 136)
136 / 3 = 45.333333333333 (the remainder is 1, so 3 is not a divisor of 136)
...
136 / 10 = 13.6 (the remainder is 6, so 10 is not a divisor of 136)
136 / 11 = 12.363636363636 (the remainder is 4, so 11 is not a divisor of 136)