What are the divisors of 152?

1, 2, 4, 8, 19, 38, 76, 152

There is a total of 8 positive divisors.
The sum of these divisors is 300.
The arithmetic mean is 37.5.

6 even divisors

2, 4, 8, 38, 76, 152

2 odd divisors

1, 19

How to compute the divisors of 152?

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 152 by each of the numbers from 1 to 152 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)

152 / 1 = 152 (the remainder is 0, so 1 is a divisor of 152)
152 / 2 = 76 (the remainder is 0, so 2 is a divisor of 152)
152 / 3 = 50.666666666667 (the remainder is 2, so 3 is not a divisor of 152)
...
152 / 151 = 1.0066225165563 (the remainder is 1, so 151 is not a divisor of 152)
152 / 152 = 1 (the remainder is 0, so 152 is a divisor of 152)

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 152 (i.e. 12.328828005938). 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 $\frac{N}{d} = D$ )

152 / 1 = 152 (the remainder is 0, so 1 and 152 are divisors of 152)
152 / 2 = 76 (the remainder is 0, so 2 and 76 are divisors of 152)
152 / 3 = 50.666666666667 (the remainder is 2, so 3 is not a divisor of 152)
...
152 / 11 = 13.818181818182 (the remainder is 9, so 11 is not a divisor of 152)
152 / 12 = 12.666666666667 (the remainder is 8, so 12 is not a divisor of 152)