What are the divisors of 1384?

1, 2, 4, 8, 173, 346, 692, 1384

There is a total of 8 positive divisors.
The sum of these divisors is 2610.
The arithmetic mean is 326.25.

6 even divisors

2, 4, 8, 346, 692, 1384

2 odd divisors

1, 173

How to compute the divisors of 1384?

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 1384 by each of the numbers from 1 to 1384 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)

1384 / 1 = 1384 (the remainder is 0, so 1 is a divisor of 1384)
1384 / 2 = 692 (the remainder is 0, so 2 is a divisor of 1384)
1384 / 3 = 461.33333333333 (the remainder is 1, so 3 is not a divisor of 1384)
...
1384 / 1383 = 1.000723065799 (the remainder is 1, so 1383 is not a divisor of 1384)
1384 / 1384 = 1 (the remainder is 0, so 1384 is a divisor of 1384)

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 1384 (i.e. 37.202150475477). 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 $\frac{N}{d} = D$ )

1384 / 1 = 1384 (the remainder is 0, so 1 and 1384 are divisors of 1384)
1384 / 2 = 692 (the remainder is 0, so 2 and 692 are divisors of 1384)
1384 / 3 = 461.33333333333 (the remainder is 1, so 3 is not a divisor of 1384)
...
1384 / 36 = 38.444444444444 (the remainder is 16, so 36 is not a divisor of 1384)
1384 / 37 = 37.405405405405 (the remainder is 15, so 37 is not a divisor of 1384)