What are the divisors of 134?

1, 2, 67, 134

There is a total of 4 positive divisors.
The sum of these divisors is 204.
The arithmetic mean is 51.

2 even divisors

2, 134

2 odd divisors

1, 67

How to compute the divisors of 134?

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 134 by each of the numbers from 1 to 134 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)

134 / 1 = 134 (the remainder is 0, so 1 is a divisor of 134)
134 / 2 = 67 (the remainder is 0, so 2 is a divisor of 134)
134 / 3 = 44.666666666667 (the remainder is 2, so 3 is not a divisor of 134)
...
134 / 133 = 1.0075187969925 (the remainder is 1, so 133 is not a divisor of 134)
134 / 134 = 1 (the remainder is 0, so 134 is a divisor of 134)

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 134 (i.e. 11.57583690279). 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 $\frac{N}{d} = D$ )

134 / 1 = 134 (the remainder is 0, so 1 and 134 are divisors of 134)
134 / 2 = 67 (the remainder is 0, so 2 and 67 are divisors of 134)
134 / 3 = 44.666666666667 (the remainder is 2, so 3 is not a divisor of 134)
...
134 / 10 = 13.4 (the remainder is 4, so 10 is not a divisor of 134)
134 / 11 = 12.181818181818 (the remainder is 2, so 11 is not a divisor of 134)