What are the divisors of 1151?

1, 1151

There is a total of 2 positive divisors.
The sum of these divisors is 1152.
The arithmetic mean is 576.

2 odd divisors

1, 1151

How to compute the divisors of 1151?

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 1151 by each of the numbers from 1 to 1151 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)

1151 / 1 = 1151 (the remainder is 0, so 1 is a divisor of 1151)
1151 / 2 = 575.5 (the remainder is 1, so 2 is not a divisor of 1151)
1151 / 3 = 383.66666666667 (the remainder is 2, so 3 is not a divisor of 1151)
...
1151 / 1150 = 1.0008695652174 (the remainder is 1, so 1150 is not a divisor of 1151)
1151 / 1151 = 1 (the remainder is 0, so 1151 is a divisor of 1151)

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 1151 (i.e. 33.926390907375). 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 $\frac{N}{d} = D$ )

1151 / 1 = 1151 (the remainder is 0, so 1 and 1151 are divisors of 1151)
1151 / 2 = 575.5 (the remainder is 1, so 2 is not a divisor of 1151)
1151 / 3 = 383.66666666667 (the remainder is 2, so 3 is not a divisor of 1151)
...
1151 / 32 = 35.96875 (the remainder is 31, so 32 is not a divisor of 1151)
1151 / 33 = 34.878787878788 (the remainder is 29, so 33 is not a divisor of 1151)