What are the divisors of 1376?

1, 2, 4, 8, 16, 32, 43, 86, 172, 344, 688, 1376

There is a total of 12 positive divisors.
The sum of these divisors is 2772.
The arithmetic mean is 231.

10 even divisors

2, 4, 8, 16, 32, 86, 172, 344, 688, 1376

2 odd divisors

1, 43

How to compute the divisors of 1376?

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 1376 by each of the numbers from 1 to 1376 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)

1376 / 1 = 1376 (the remainder is 0, so 1 is a divisor of 1376)
1376 / 2 = 688 (the remainder is 0, so 2 is a divisor of 1376)
1376 / 3 = 458.66666666667 (the remainder is 2, so 3 is not a divisor of 1376)
...
1376 / 1375 = 1.0007272727273 (the remainder is 1, so 1375 is not a divisor of 1376)
1376 / 1376 = 1 (the remainder is 0, so 1376 is a divisor of 1376)

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 1376 (i.e. 37.094473981983). 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 $\frac{N}{d} = D$ )

1376 / 1 = 1376 (the remainder is 0, so 1 and 1376 are divisors of 1376)
1376 / 2 = 688 (the remainder is 0, so 2 and 688 are divisors of 1376)
1376 / 3 = 458.66666666667 (the remainder is 2, so 3 is not a divisor of 1376)
...
1376 / 36 = 38.222222222222 (the remainder is 8, so 36 is not a divisor of 1376)
1376 / 37 = 37.189189189189 (the remainder is 7, so 37 is not a divisor of 1376)