What are the divisors of 1532?

1, 2, 4, 383, 766, 1532

There is a total of 6 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 448.

4 even divisors

2, 4, 766, 1532

2 odd divisors

1, 383

How to compute the divisors of 1532?

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 1532 by each of the numbers from 1 to 1532 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)

1532 / 1 = 1532 (the remainder is 0, so 1 is a divisor of 1532)
1532 / 2 = 766 (the remainder is 0, so 2 is a divisor of 1532)
1532 / 3 = 510.66666666667 (the remainder is 2, so 3 is not a divisor of 1532)
...
1532 / 1531 = 1.0006531678641 (the remainder is 1, so 1531 is not a divisor of 1532)
1532 / 1532 = 1 (the remainder is 0, so 1532 is a divisor of 1532)

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 1532 (i.e. 39.140771581562). 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 $\frac{N}{d} = D$ )

1532 / 1 = 1532 (the remainder is 0, so 1 and 1532 are divisors of 1532)
1532 / 2 = 766 (the remainder is 0, so 2 and 766 are divisors of 1532)
1532 / 3 = 510.66666666667 (the remainder is 2, so 3 is not a divisor of 1532)
...
1532 / 38 = 40.315789473684 (the remainder is 12, so 38 is not a divisor of 1532)
1532 / 39 = 39.282051282051 (the remainder is 11, so 39 is not a divisor of 1532)