What are the divisors of 1529?

1, 11, 139, 1529

There is a total of 4 positive divisors.
The sum of these divisors is 1680.
The arithmetic mean is 420.

4 odd divisors

1, 11, 139, 1529

How to compute the divisors of 1529?

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 1529 by each of the numbers from 1 to 1529 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)

1529 / 1 = 1529 (the remainder is 0, so 1 is a divisor of 1529)
1529 / 2 = 764.5 (the remainder is 1, so 2 is not a divisor of 1529)
1529 / 3 = 509.66666666667 (the remainder is 2, so 3 is not a divisor of 1529)
...
1529 / 1528 = 1.0006544502618 (the remainder is 1, so 1528 is not a divisor of 1529)
1529 / 1529 = 1 (the remainder is 0, so 1529 is a divisor of 1529)

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 1529 (i.e. 39.102429592034). 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 $\frac{N}{d} = D$ )

1529 / 1 = 1529 (the remainder is 0, so 1 and 1529 are divisors of 1529)
1529 / 2 = 764.5 (the remainder is 1, so 2 is not a divisor of 1529)
1529 / 3 = 509.66666666667 (the remainder is 2, so 3 is not a divisor of 1529)
...
1529 / 38 = 40.236842105263 (the remainder is 9, so 38 is not a divisor of 1529)
1529 / 39 = 39.205128205128 (the remainder is 8, so 39 is not a divisor of 1529)