What are the divisors of 1055?

1, 5, 211, 1055

There is a total of 4 positive divisors.
The sum of these divisors is 1272.
The arithmetic mean is 318.

4 odd divisors

1, 5, 211, 1055

How to compute the divisors of 1055?

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 1055 by each of the numbers from 1 to 1055 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)

1055 / 1 = 1055 (the remainder is 0, so 1 is a divisor of 1055)
1055 / 2 = 527.5 (the remainder is 1, so 2 is not a divisor of 1055)
1055 / 3 = 351.66666666667 (the remainder is 2, so 3 is not a divisor of 1055)
...
1055 / 1054 = 1.0009487666034 (the remainder is 1, so 1054 is not a divisor of 1055)
1055 / 1055 = 1 (the remainder is 0, so 1055 is a divisor of 1055)

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 1055 (i.e. 32.480763537823). 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 $\frac{N}{d} = D$ )

1055 / 1 = 1055 (the remainder is 0, so 1 and 1055 are divisors of 1055)
1055 / 2 = 527.5 (the remainder is 1, so 2 is not a divisor of 1055)
1055 / 3 = 351.66666666667 (the remainder is 2, so 3 is not a divisor of 1055)
...
1055 / 31 = 34.032258064516 (the remainder is 1, so 31 is not a divisor of 1055)
1055 / 32 = 32.96875 (the remainder is 31, so 32 is not a divisor of 1055)