What are the divisors of 1416?

1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416

There is a total of 16 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 225.

12 even divisors

2, 4, 6, 8, 12, 24, 118, 236, 354, 472, 708, 1416

4 odd divisors

1, 3, 59, 177

How to compute the divisors of 1416?

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 1416 by each of the numbers from 1 to 1416 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)

1416 / 1 = 1416 (the remainder is 0, so 1 is a divisor of 1416)
1416 / 2 = 708 (the remainder is 0, so 2 is a divisor of 1416)
1416 / 3 = 472 (the remainder is 0, so 3 is a divisor of 1416)
...
1416 / 1415 = 1.0007067137809 (the remainder is 1, so 1415 is not a divisor of 1416)
1416 / 1416 = 1 (the remainder is 0, so 1416 is a divisor of 1416)

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 1416 (i.e. 37.629775444454). 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 $\frac{N}{d} = D$ )

1416 / 1 = 1416 (the remainder is 0, so 1 and 1416 are divisors of 1416)
1416 / 2 = 708 (the remainder is 0, so 2 and 708 are divisors of 1416)
1416 / 3 = 472 (the remainder is 0, so 3 and 472 are divisors of 1416)
...
1416 / 36 = 39.333333333333 (the remainder is 12, so 36 is not a divisor of 1416)
1416 / 37 = 38.27027027027 (the remainder is 10, so 37 is not a divisor of 1416)