What are the divisors of 1479?

1, 3, 17, 29, 51, 87, 493, 1479

There is a total of 8 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 270.

8 odd divisors

1, 3, 17, 29, 51, 87, 493, 1479

How to compute the divisors of 1479?

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 1479 by each of the numbers from 1 to 1479 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)

1479 / 1 = 1479 (the remainder is 0, so 1 is a divisor of 1479)
1479 / 2 = 739.5 (the remainder is 1, so 2 is not a divisor of 1479)
1479 / 3 = 493 (the remainder is 0, so 3 is a divisor of 1479)
...
1479 / 1478 = 1.0006765899865 (the remainder is 1, so 1478 is not a divisor of 1479)
1479 / 1479 = 1 (the remainder is 0, so 1479 is a divisor of 1479)

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 1479 (i.e. 38.457769046059). 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 $\frac{N}{d} = D$ )

1479 / 1 = 1479 (the remainder is 0, so 1 and 1479 are divisors of 1479)
1479 / 2 = 739.5 (the remainder is 1, so 2 is not a divisor of 1479)
1479 / 3 = 493 (the remainder is 0, so 3 and 493 are divisors of 1479)
...
1479 / 37 = 39.972972972973 (the remainder is 36, so 37 is not a divisor of 1479)
1479 / 38 = 38.921052631579 (the remainder is 35, so 38 is not a divisor of 1479)