What are the divisors of 2213?

1, 2213

There is a total of 2 positive divisors.
The sum of these divisors is 2214.
The arithmetic mean is 1107.

2 odd divisors

1, 2213

How to compute the divisors of 2213?

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 2213 by each of the numbers from 1 to 2213 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)

2213 / 1 = 2213 (the remainder is 0, so 1 is a divisor of 2213)
2213 / 2 = 1106.5 (the remainder is 1, so 2 is not a divisor of 2213)
2213 / 3 = 737.66666666667 (the remainder is 2, so 3 is not a divisor of 2213)
...
2213 / 2212 = 1.000452079566 (the remainder is 1, so 2212 is not a divisor of 2213)
2213 / 2213 = 1 (the remainder is 0, so 2213 is a divisor of 2213)

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 2213 (i.e. 47.042533945356). 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 $\frac{N}{d} = D$ )

2213 / 1 = 2213 (the remainder is 0, so 1 and 2213 are divisors of 2213)
2213 / 2 = 1106.5 (the remainder is 1, so 2 is not a divisor of 2213)
2213 / 3 = 737.66666666667 (the remainder is 2, so 3 is not a divisor of 2213)
...
2213 / 46 = 48.108695652174 (the remainder is 5, so 46 is not a divisor of 2213)
2213 / 47 = 47.085106382979 (the remainder is 4, so 47 is not a divisor of 2213)