What are the divisors of 146?

1, 2, 73, 146

There is a total of 4 positive divisors.
The sum of these divisors is 222.
The arithmetic mean is 55.5.

2 even divisors

2, 146

2 odd divisors

1, 73

How to compute the divisors of 146?

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 146 by each of the numbers from 1 to 146 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)

146 / 1 = 146 (the remainder is 0, so 1 is a divisor of 146)
146 / 2 = 73 (the remainder is 0, so 2 is a divisor of 146)
146 / 3 = 48.666666666667 (the remainder is 2, so 3 is not a divisor of 146)
...
146 / 145 = 1.0068965517241 (the remainder is 1, so 145 is not a divisor of 146)
146 / 146 = 1 (the remainder is 0, so 146 is a divisor of 146)

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 146 (i.e. 12.083045973595). 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 $\frac{N}{d} = D$ )

146 / 1 = 146 (the remainder is 0, so 1 and 146 are divisors of 146)
146 / 2 = 73 (the remainder is 0, so 2 and 73 are divisors of 146)
146 / 3 = 48.666666666667 (the remainder is 2, so 3 is not a divisor of 146)
...
146 / 11 = 13.272727272727 (the remainder is 3, so 11 is not a divisor of 146)
146 / 12 = 12.166666666667 (the remainder is 2, so 12 is not a divisor of 146)