What are the divisors of 149?

1, 149

There is a total of 2 positive divisors.
The sum of these divisors is 150.
The arithmetic mean is 75.

2 odd divisors

1, 149

How to compute the divisors of 149?

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 149 by each of the numbers from 1 to 149 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)

149 / 1 = 149 (the remainder is 0, so 1 is a divisor of 149)
149 / 2 = 74.5 (the remainder is 1, so 2 is not a divisor of 149)
149 / 3 = 49.666666666667 (the remainder is 2, so 3 is not a divisor of 149)
...
149 / 148 = 1.0067567567568 (the remainder is 1, so 148 is not a divisor of 149)
149 / 149 = 1 (the remainder is 0, so 149 is a divisor of 149)

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 149 (i.e. 12.206555615734). 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 $\frac{N}{d} = D$ )

149 / 1 = 149 (the remainder is 0, so 1 and 149 are divisors of 149)
149 / 2 = 74.5 (the remainder is 1, so 2 is not a divisor of 149)
149 / 3 = 49.666666666667 (the remainder is 2, so 3 is not a divisor of 149)
...
149 / 11 = 13.545454545455 (the remainder is 6, so 11 is not a divisor of 149)
149 / 12 = 12.416666666667 (the remainder is 5, so 12 is not a divisor of 149)