What are the divisors of 1343?

1, 17, 79, 1343

There is a total of 4 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 360.

4 odd divisors

1, 17, 79, 1343

How to compute the divisors of 1343?

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 1343 by each of the numbers from 1 to 1343 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)

1343 / 1 = 1343 (the remainder is 0, so 1 is a divisor of 1343)
1343 / 2 = 671.5 (the remainder is 1, so 2 is not a divisor of 1343)
1343 / 3 = 447.66666666667 (the remainder is 2, so 3 is not a divisor of 1343)
...
1343 / 1342 = 1.0007451564829 (the remainder is 1, so 1342 is not a divisor of 1343)
1343 / 1343 = 1 (the remainder is 0, so 1343 is a divisor of 1343)

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 1343 (i.e. 36.646964403617). 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 $\frac{N}{d} = D$ )

1343 / 1 = 1343 (the remainder is 0, so 1 and 1343 are divisors of 1343)
1343 / 2 = 671.5 (the remainder is 1, so 2 is not a divisor of 1343)
1343 / 3 = 447.66666666667 (the remainder is 2, so 3 is not a divisor of 1343)
...
1343 / 35 = 38.371428571429 (the remainder is 13, so 35 is not a divisor of 1343)
1343 / 36 = 37.305555555556 (the remainder is 11, so 36 is not a divisor of 1343)