What are the divisors of 1425?

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475, 1425

There is a total of 12 positive divisors.
The sum of these divisors is 2480.
The arithmetic mean is 206.66666666667.

12 odd divisors

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475, 1425

How to compute the divisors of 1425?

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 1425 by each of the numbers from 1 to 1425 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)

1425 / 1 = 1425 (the remainder is 0, so 1 is a divisor of 1425)
1425 / 2 = 712.5 (the remainder is 1, so 2 is not a divisor of 1425)
1425 / 3 = 475 (the remainder is 0, so 3 is a divisor of 1425)
...
1425 / 1424 = 1.000702247191 (the remainder is 1, so 1424 is not a divisor of 1425)
1425 / 1425 = 1 (the remainder is 0, so 1425 is a divisor of 1425)

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 1425 (i.e. 37.749172176354). 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 $\frac{N}{d} = D$ )

1425 / 1 = 1425 (the remainder is 0, so 1 and 1425 are divisors of 1425)
1425 / 2 = 712.5 (the remainder is 1, so 2 is not a divisor of 1425)
1425 / 3 = 475 (the remainder is 0, so 3 and 475 are divisors of 1425)
...
1425 / 36 = 39.583333333333 (the remainder is 21, so 36 is not a divisor of 1425)
1425 / 37 = 38.513513513514 (the remainder is 19, so 37 is not a divisor of 1425)