What are the divisors of 1435?

1, 5, 7, 35, 41, 205, 287, 1435

There is a total of 8 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 252.

8 odd divisors

1, 5, 7, 35, 41, 205, 287, 1435

How to compute the divisors of 1435?

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 1435 by each of the numbers from 1 to 1435 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)

1435 / 1 = 1435 (the remainder is 0, so 1 is a divisor of 1435)
1435 / 2 = 717.5 (the remainder is 1, so 2 is not a divisor of 1435)
1435 / 3 = 478.33333333333 (the remainder is 1, so 3 is not a divisor of 1435)
...
1435 / 1434 = 1.0006973500697 (the remainder is 1, so 1434 is not a divisor of 1435)
1435 / 1435 = 1 (the remainder is 0, so 1435 is a divisor of 1435)

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 1435 (i.e. 37.881393849752). 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 $\frac{N}{d} = D$ )

1435 / 1 = 1435 (the remainder is 0, so 1 and 1435 are divisors of 1435)
1435 / 2 = 717.5 (the remainder is 1, so 2 is not a divisor of 1435)
1435 / 3 = 478.33333333333 (the remainder is 1, so 3 is not a divisor of 1435)
...
1435 / 36 = 39.861111111111 (the remainder is 31, so 36 is not a divisor of 1435)
1435 / 37 = 38.783783783784 (the remainder is 29, so 37 is not a divisor of 1435)