What are the divisors of 1106?

1, 2, 7, 14, 79, 158, 553, 1106

There is a total of 8 positive divisors.
The sum of these divisors is 1920.
The arithmetic mean is 240.

4 even divisors

2, 14, 158, 1106

4 odd divisors

1, 7, 79, 553

How to compute the divisors of 1106?

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 1106 by each of the numbers from 1 to 1106 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)

1106 / 1 = 1106 (the remainder is 0, so 1 is a divisor of 1106)
1106 / 2 = 553 (the remainder is 0, so 2 is a divisor of 1106)
1106 / 3 = 368.66666666667 (the remainder is 2, so 3 is not a divisor of 1106)
...
1106 / 1105 = 1.0009049773756 (the remainder is 1, so 1105 is not a divisor of 1106)
1106 / 1106 = 1 (the remainder is 0, so 1106 is a divisor of 1106)

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 1106 (i.e. 33.256578296632). 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 $\frac{N}{d} = D$ )

1106 / 1 = 1106 (the remainder is 0, so 1 and 1106 are divisors of 1106)
1106 / 2 = 553 (the remainder is 0, so 2 and 553 are divisors of 1106)
1106 / 3 = 368.66666666667 (the remainder is 2, so 3 is not a divisor of 1106)
...
1106 / 32 = 34.5625 (the remainder is 18, so 32 is not a divisor of 1106)
1106 / 33 = 33.515151515152 (the remainder is 17, so 33 is not a divisor of 1106)