What are the divisors of 1222?

1, 2, 13, 26, 47, 94, 611, 1222

There is a total of 8 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 252.

4 even divisors

2, 26, 94, 1222

4 odd divisors

1, 13, 47, 611

How to compute the divisors of 1222?

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 1222 by each of the numbers from 1 to 1222 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)

1222 / 1 = 1222 (the remainder is 0, so 1 is a divisor of 1222)
1222 / 2 = 611 (the remainder is 0, so 2 is a divisor of 1222)
1222 / 3 = 407.33333333333 (the remainder is 1, so 3 is not a divisor of 1222)
...
1222 / 1221 = 1.000819000819 (the remainder is 1, so 1221 is not a divisor of 1222)
1222 / 1222 = 1 (the remainder is 0, so 1222 is a divisor of 1222)

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 1222 (i.e. 34.957116585897). 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 $\frac{N}{d} = D$ )

1222 / 1 = 1222 (the remainder is 0, so 1 and 1222 are divisors of 1222)
1222 / 2 = 611 (the remainder is 0, so 2 and 611 are divisors of 1222)
1222 / 3 = 407.33333333333 (the remainder is 1, so 3 is not a divisor of 1222)
...
1222 / 33 = 37.030303030303 (the remainder is 1, so 33 is not a divisor of 1222)
1222 / 34 = 35.941176470588 (the remainder is 32, so 34 is not a divisor of 1222)