What are the divisors of 148?

1, 2, 4, 37, 74, 148

There is a total of 6 positive divisors.
The sum of these divisors is 266.
The arithmetic mean is 44.333333333333.

4 even divisors

2, 4, 74, 148

2 odd divisors

1, 37

How to compute the divisors of 148?

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 148 by each of the numbers from 1 to 148 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)

148 / 1 = 148 (the remainder is 0, so 1 is a divisor of 148)
148 / 2 = 74 (the remainder is 0, so 2 is a divisor of 148)
148 / 3 = 49.333333333333 (the remainder is 1, so 3 is not a divisor of 148)
...
148 / 147 = 1.0068027210884 (the remainder is 1, so 147 is not a divisor of 148)
148 / 148 = 1 (the remainder is 0, so 148 is a divisor of 148)

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 148 (i.e. 12.165525060596). 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 $\frac{N}{d} = D$ )

148 / 1 = 148 (the remainder is 0, so 1 and 148 are divisors of 148)
148 / 2 = 74 (the remainder is 0, so 2 and 74 are divisors of 148)
148 / 3 = 49.333333333333 (the remainder is 1, so 3 is not a divisor of 148)
...
148 / 11 = 13.454545454545 (the remainder is 5, so 11 is not a divisor of 148)
148 / 12 = 12.333333333333 (the remainder is 4, so 12 is not a divisor of 148)