What are the divisors of 1388?

1, 2, 4, 347, 694, 1388

There is a total of 6 positive divisors.
The sum of these divisors is 2436.
The arithmetic mean is 406.

4 even divisors

2, 4, 694, 1388

2 odd divisors

1, 347

How to compute the divisors of 1388?

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 1388 by each of the numbers from 1 to 1388 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)

1388 / 1 = 1388 (the remainder is 0, so 1 is a divisor of 1388)
1388 / 2 = 694 (the remainder is 0, so 2 is a divisor of 1388)
1388 / 3 = 462.66666666667 (the remainder is 2, so 3 is not a divisor of 1388)
...
1388 / 1387 = 1.0007209805335 (the remainder is 1, so 1387 is not a divisor of 1388)
1388 / 1388 = 1 (the remainder is 0, so 1388 is a divisor of 1388)

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 1388 (i.e. 37.255872020394). 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 $\frac{N}{d} = D$ )

1388 / 1 = 1388 (the remainder is 0, so 1 and 1388 are divisors of 1388)
1388 / 2 = 694 (the remainder is 0, so 2 and 694 are divisors of 1388)
1388 / 3 = 462.66666666667 (the remainder is 2, so 3 is not a divisor of 1388)
...
1388 / 36 = 38.555555555556 (the remainder is 20, so 36 is not a divisor of 1388)
1388 / 37 = 37.513513513514 (the remainder is 19, so 37 is not a divisor of 1388)