What are the divisors of 2210?

1, 2, 5, 10, 13, 17, 26, 34, 65, 85, 130, 170, 221, 442, 1105, 2210

There is a total of 16 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 283.5.

8 even divisors

2, 10, 26, 34, 130, 170, 442, 2210

8 odd divisors

1, 5, 13, 17, 65, 85, 221, 1105

How to compute the divisors of 2210?

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 2210 by each of the numbers from 1 to 2210 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)

2210 / 1 = 2210 (the remainder is 0, so 1 is a divisor of 2210)
2210 / 2 = 1105 (the remainder is 0, so 2 is a divisor of 2210)
2210 / 3 = 736.66666666667 (the remainder is 2, so 3 is not a divisor of 2210)
...
2210 / 2209 = 1.0004526935265 (the remainder is 1, so 2209 is not a divisor of 2210)
2210 / 2210 = 1 (the remainder is 0, so 2210 is a divisor of 2210)

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 2210 (i.e. 47.010637094173). 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 $\frac{N}{d} = D$ )

2210 / 1 = 2210 (the remainder is 0, so 1 and 2210 are divisors of 2210)
2210 / 2 = 1105 (the remainder is 0, so 2 and 1105 are divisors of 2210)
2210 / 3 = 736.66666666667 (the remainder is 2, so 3 is not a divisor of 2210)
...
2210 / 46 = 48.04347826087 (the remainder is 2, so 46 is not a divisor of 2210)
2210 / 47 = 47.021276595745 (the remainder is 1, so 47 is not a divisor of 2210)