What are the divisors of 1127?

1, 7, 23, 49, 161, 1127

There is a total of 6 positive divisors.
The sum of these divisors is 1368.
The arithmetic mean is 228.

6 odd divisors

1, 7, 23, 49, 161, 1127

How to compute the divisors of 1127?

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 1127 by each of the numbers from 1 to 1127 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)

1127 / 1 = 1127 (the remainder is 0, so 1 is a divisor of 1127)
1127 / 2 = 563.5 (the remainder is 1, so 2 is not a divisor of 1127)
1127 / 3 = 375.66666666667 (the remainder is 2, so 3 is not a divisor of 1127)
...
1127 / 1126 = 1.0008880994671 (the remainder is 1, so 1126 is not a divisor of 1127)
1127 / 1127 = 1 (the remainder is 0, so 1127 is a divisor of 1127)

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 1127 (i.e. 33.570820663189). 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 $\frac{N}{d} = D$ )

1127 / 1 = 1127 (the remainder is 0, so 1 and 1127 are divisors of 1127)
1127 / 2 = 563.5 (the remainder is 1, so 2 is not a divisor of 1127)
1127 / 3 = 375.66666666667 (the remainder is 2, so 3 is not a divisor of 1127)
...
1127 / 32 = 35.21875 (the remainder is 7, so 32 is not a divisor of 1127)
1127 / 33 = 34.151515151515 (the remainder is 5, so 33 is not a divisor of 1127)