What are the divisors of 1445?

1, 5, 17, 85, 289, 1445

There is a total of 6 positive divisors.
The sum of these divisors is 1842.
The arithmetic mean is 307.

6 odd divisors

1, 5, 17, 85, 289, 1445

How to compute the divisors of 1445?

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 1445 by each of the numbers from 1 to 1445 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)

1445 / 1 = 1445 (the remainder is 0, so 1 is a divisor of 1445)
1445 / 2 = 722.5 (the remainder is 1, so 2 is not a divisor of 1445)
1445 / 3 = 481.66666666667 (the remainder is 2, so 3 is not a divisor of 1445)
...
1445 / 1444 = 1.0006925207756 (the remainder is 1, so 1444 is not a divisor of 1445)
1445 / 1445 = 1 (the remainder is 0, so 1445 is a divisor of 1445)

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 1445 (i.e. 38.013155617496). 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 $\frac{N}{d} = D$ )

1445 / 1 = 1445 (the remainder is 0, so 1 and 1445 are divisors of 1445)
1445 / 2 = 722.5 (the remainder is 1, so 2 is not a divisor of 1445)
1445 / 3 = 481.66666666667 (the remainder is 2, so 3 is not a divisor of 1445)
...
1445 / 37 = 39.054054054054 (the remainder is 2, so 37 is not a divisor of 1445)
1445 / 38 = 38.026315789474 (the remainder is 1, so 38 is not a divisor of 1445)