What are the divisors of 1319?

1, 1319

There is a total of 2 positive divisors.
The sum of these divisors is 1320.
The arithmetic mean is 660.

2 odd divisors

1, 1319

How to compute the divisors of 1319?

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 1319 by each of the numbers from 1 to 1319 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)

1319 / 1 = 1319 (the remainder is 0, so 1 is a divisor of 1319)
1319 / 2 = 659.5 (the remainder is 1, so 2 is not a divisor of 1319)
1319 / 3 = 439.66666666667 (the remainder is 2, so 3 is not a divisor of 1319)
...
1319 / 1318 = 1.0007587253414 (the remainder is 1, so 1318 is not a divisor of 1319)
1319 / 1319 = 1 (the remainder is 0, so 1319 is a divisor of 1319)

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 1319 (i.e. 36.31803959467). 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 $\frac{N}{d} = D$ )

1319 / 1 = 1319 (the remainder is 0, so 1 and 1319 are divisors of 1319)
1319 / 2 = 659.5 (the remainder is 1, so 2 is not a divisor of 1319)
1319 / 3 = 439.66666666667 (the remainder is 2, so 3 is not a divisor of 1319)
...
1319 / 35 = 37.685714285714 (the remainder is 24, so 35 is not a divisor of 1319)
1319 / 36 = 36.638888888889 (the remainder is 23, so 36 is not a divisor of 1319)