What are the divisors of 352?

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352

There is a total of 12 positive divisors.
The sum of these divisors is 756.
The arithmetic mean is 63.

10 even divisors

2, 4, 8, 16, 22, 32, 44, 88, 176, 352

2 odd divisors

1, 11

How to compute the divisors of 352?

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 352 by each of the numbers from 1 to 352 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)

352 / 1 = 352 (the remainder is 0, so 1 is a divisor of 352)
352 / 2 = 176 (the remainder is 0, so 2 is a divisor of 352)
352 / 3 = 117.33333333333 (the remainder is 1, so 3 is not a divisor of 352)
...
352 / 351 = 1.002849002849 (the remainder is 1, so 351 is not a divisor of 352)
352 / 352 = 1 (the remainder is 0, so 352 is a divisor of 352)

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 352 (i.e. 18.761663039294). 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 $\frac{N}{d} = D$ )

352 / 1 = 352 (the remainder is 0, so 1 and 352 are divisors of 352)
352 / 2 = 176 (the remainder is 0, so 2 and 176 are divisors of 352)
352 / 3 = 117.33333333333 (the remainder is 1, so 3 is not a divisor of 352)
...
352 / 17 = 20.705882352941 (the remainder is 12, so 17 is not a divisor of 352)
352 / 18 = 19.555555555556 (the remainder is 10, so 18 is not a divisor of 352)