What are the divisors of 1455?

1, 3, 5, 15, 97, 291, 485, 1455

There is a total of 8 positive divisors.
The sum of these divisors is 2352.
The arithmetic mean is 294.

8 odd divisors

1, 3, 5, 15, 97, 291, 485, 1455

How to compute the divisors of 1455?

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 1455 by each of the numbers from 1 to 1455 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)

1455 / 1 = 1455 (the remainder is 0, so 1 is a divisor of 1455)
1455 / 2 = 727.5 (the remainder is 1, so 2 is not a divisor of 1455)
1455 / 3 = 485 (the remainder is 0, so 3 is a divisor of 1455)
...
1455 / 1454 = 1.0006877579092 (the remainder is 1, so 1454 is not a divisor of 1455)
1455 / 1455 = 1 (the remainder is 0, so 1455 is a divisor of 1455)

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 1455 (i.e. 38.144462245521). 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 $\frac{N}{d} = D$ )

1455 / 1 = 1455 (the remainder is 0, so 1 and 1455 are divisors of 1455)
1455 / 2 = 727.5 (the remainder is 1, so 2 is not a divisor of 1455)
1455 / 3 = 485 (the remainder is 0, so 3 and 485 are divisors of 1455)
...
1455 / 37 = 39.324324324324 (the remainder is 12, so 37 is not a divisor of 1455)
1455 / 38 = 38.289473684211 (the remainder is 11, so 38 is not a divisor of 1455)