What are the divisors of 2224?

1, 2, 4, 8, 16, 139, 278, 556, 1112, 2224

There is a total of 10 positive divisors.
The sum of these divisors is 4340.
The arithmetic mean is 434.

8 even divisors

2, 4, 8, 16, 278, 556, 1112, 2224

2 odd divisors

1, 139

How to compute the divisors of 2224?

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 2224 by each of the numbers from 1 to 2224 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)

2224 / 1 = 2224 (the remainder is 0, so 1 is a divisor of 2224)
2224 / 2 = 1112 (the remainder is 0, so 2 is a divisor of 2224)
2224 / 3 = 741.33333333333 (the remainder is 1, so 3 is not a divisor of 2224)
...
2224 / 2223 = 1.0004498425551 (the remainder is 1, so 2223 is not a divisor of 2224)
2224 / 2224 = 1 (the remainder is 0, so 2224 is a divisor of 2224)

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 2224 (i.e. 47.159304490206). 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 $\frac{N}{d} = D$ )

2224 / 1 = 2224 (the remainder is 0, so 1 and 2224 are divisors of 2224)
2224 / 2 = 1112 (the remainder is 0, so 2 and 1112 are divisors of 2224)
2224 / 3 = 741.33333333333 (the remainder is 1, so 3 is not a divisor of 2224)
...
2224 / 46 = 48.347826086957 (the remainder is 16, so 46 is not a divisor of 2224)
2224 / 47 = 47.31914893617 (the remainder is 15, so 47 is not a divisor of 2224)