What are the divisors of 1419?

1, 3, 11, 33, 43, 129, 473, 1419

There is a total of 8 positive divisors.
The sum of these divisors is 2112.
The arithmetic mean is 264.

8 odd divisors

1, 3, 11, 33, 43, 129, 473, 1419

How to compute the divisors of 1419?

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 1419 by each of the numbers from 1 to 1419 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)

1419 / 1 = 1419 (the remainder is 0, so 1 is a divisor of 1419)
1419 / 2 = 709.5 (the remainder is 1, so 2 is not a divisor of 1419)
1419 / 3 = 473 (the remainder is 0, so 3 is a divisor of 1419)
...
1419 / 1418 = 1.0007052186178 (the remainder is 1, so 1418 is not a divisor of 1419)
1419 / 1419 = 1 (the remainder is 0, so 1419 is a divisor of 1419)

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 1419 (i.e. 37.669616403675). 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 $\frac{N}{d} = D$ )

1419 / 1 = 1419 (the remainder is 0, so 1 and 1419 are divisors of 1419)
1419 / 2 = 709.5 (the remainder is 1, so 2 is not a divisor of 1419)
1419 / 3 = 473 (the remainder is 0, so 3 and 473 are divisors of 1419)
...
1419 / 36 = 39.416666666667 (the remainder is 15, so 36 is not a divisor of 1419)
1419 / 37 = 38.351351351351 (the remainder is 13, so 37 is not a divisor of 1419)