What are the divisors of 1506?

1, 2, 3, 6, 251, 502, 753, 1506

There is a total of 8 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 378.

4 even divisors

2, 6, 502, 1506

4 odd divisors

1, 3, 251, 753

How to compute the divisors of 1506?

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 1506 by each of the numbers from 1 to 1506 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)

1506 / 1 = 1506 (the remainder is 0, so 1 is a divisor of 1506)
1506 / 2 = 753 (the remainder is 0, so 2 is a divisor of 1506)
1506 / 3 = 502 (the remainder is 0, so 3 is a divisor of 1506)
...
1506 / 1505 = 1.0006644518272 (the remainder is 1, so 1505 is not a divisor of 1506)
1506 / 1506 = 1 (the remainder is 0, so 1506 is a divisor of 1506)

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 1506 (i.e. 38.807215823865). 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 $\frac{N}{d} = D$ )

1506 / 1 = 1506 (the remainder is 0, so 1 and 1506 are divisors of 1506)
1506 / 2 = 753 (the remainder is 0, so 2 and 753 are divisors of 1506)
1506 / 3 = 502 (the remainder is 0, so 3 and 502 are divisors of 1506)
...
1506 / 37 = 40.702702702703 (the remainder is 26, so 37 is not a divisor of 1506)
1506 / 38 = 39.631578947368 (the remainder is 24, so 38 is not a divisor of 1506)