What are the divisors of 1476?

1, 2, 3, 4, 6, 9, 12, 18, 36, 41, 82, 123, 164, 246, 369, 492, 738, 1476

There is a total of 18 positive divisors.
The sum of these divisors is 3822.
The arithmetic mean is 212.33333333333.

12 even divisors

2, 4, 6, 12, 18, 36, 82, 164, 246, 492, 738, 1476

6 odd divisors

1, 3, 9, 41, 123, 369

How to compute the divisors of 1476?

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 1476 by each of the numbers from 1 to 1476 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)

1476 / 1 = 1476 (the remainder is 0, so 1 is a divisor of 1476)
1476 / 2 = 738 (the remainder is 0, so 2 is a divisor of 1476)
1476 / 3 = 492 (the remainder is 0, so 3 is a divisor of 1476)
...
1476 / 1475 = 1.0006779661017 (the remainder is 1, so 1475 is not a divisor of 1476)
1476 / 1476 = 1 (the remainder is 0, so 1476 is a divisor of 1476)

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 1476 (i.e. 38.418745424597). 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 $\frac{N}{d} = D$ )

1476 / 1 = 1476 (the remainder is 0, so 1 and 1476 are divisors of 1476)
1476 / 2 = 738 (the remainder is 0, so 2 and 738 are divisors of 1476)
1476 / 3 = 492 (the remainder is 0, so 3 and 492 are divisors of 1476)
...
1476 / 37 = 39.891891891892 (the remainder is 33, so 37 is not a divisor of 1476)
1476 / 38 = 38.842105263158 (the remainder is 32, so 38 is not a divisor of 1476)