What are the divisors of 1216?

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216

There is a total of 14 positive divisors.
The sum of these divisors is 2540.
The arithmetic mean is 181.42857142857.

12 even divisors

2, 4, 8, 16, 32, 38, 64, 76, 152, 304, 608, 1216

2 odd divisors

1, 19

How to compute the divisors of 1216?

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 1216 by each of the numbers from 1 to 1216 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)

1216 / 1 = 1216 (the remainder is 0, so 1 is a divisor of 1216)
1216 / 2 = 608 (the remainder is 0, so 2 is a divisor of 1216)
1216 / 3 = 405.33333333333 (the remainder is 1, so 3 is not a divisor of 1216)
...
1216 / 1215 = 1.0008230452675 (the remainder is 1, so 1215 is not a divisor of 1216)
1216 / 1216 = 1 (the remainder is 0, so 1216 is a divisor of 1216)

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 1216 (i.e. 34.871191548325). 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 $\frac{N}{d} = D$ )

1216 / 1 = 1216 (the remainder is 0, so 1 and 1216 are divisors of 1216)
1216 / 2 = 608 (the remainder is 0, so 2 and 608 are divisors of 1216)
1216 / 3 = 405.33333333333 (the remainder is 1, so 3 is not a divisor of 1216)
...
1216 / 33 = 36.848484848485 (the remainder is 28, so 33 is not a divisor of 1216)
1216 / 34 = 35.764705882353 (the remainder is 26, so 34 is not a divisor of 1216)