What are the divisors of 176?

1, 2, 4, 8, 11, 16, 22, 44, 88, 176

There is a total of 10 positive divisors.
The sum of these divisors is 372.
The arithmetic mean is 37.2.

8 even divisors

2, 4, 8, 16, 22, 44, 88, 176

2 odd divisors

1, 11

How to compute the divisors of 176?

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 176 by each of the numbers from 1 to 176 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)

176 / 1 = 176 (the remainder is 0, so 1 is a divisor of 176)
176 / 2 = 88 (the remainder is 0, so 2 is a divisor of 176)
176 / 3 = 58.666666666667 (the remainder is 2, so 3 is not a divisor of 176)
...
176 / 175 = 1.0057142857143 (the remainder is 1, so 175 is not a divisor of 176)
176 / 176 = 1 (the remainder is 0, so 176 is a divisor of 176)

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 176 (i.e. 13.266499161422). 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 $\frac{N}{d} = D$ )

176 / 1 = 176 (the remainder is 0, so 1 and 176 are divisors of 176)
176 / 2 = 88 (the remainder is 0, so 2 and 88 are divisors of 176)
176 / 3 = 58.666666666667 (the remainder is 2, so 3 is not a divisor of 176)
...
176 / 12 = 14.666666666667 (the remainder is 8, so 12 is not a divisor of 176)
176 / 13 = 13.538461538462 (the remainder is 7, so 13 is not a divisor of 176)