What are the divisors of 1154?

1, 2, 577, 1154

There is a total of 4 positive divisors.
The sum of these divisors is 1734.
The arithmetic mean is 433.5.

2 even divisors

2, 1154

2 odd divisors

1, 577

How to compute the divisors of 1154?

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 1154 by each of the numbers from 1 to 1154 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)

1154 / 1 = 1154 (the remainder is 0, so 1 is a divisor of 1154)
1154 / 2 = 577 (the remainder is 0, so 2 is a divisor of 1154)
1154 / 3 = 384.66666666667 (the remainder is 2, so 3 is not a divisor of 1154)
...
1154 / 1153 = 1.0008673026886 (the remainder is 1, so 1153 is not a divisor of 1154)
1154 / 1154 = 1 (the remainder is 0, so 1154 is a divisor of 1154)

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 1154 (i.e. 33.970575502926). 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 $\frac{N}{d} = D$ )

1154 / 1 = 1154 (the remainder is 0, so 1 and 1154 are divisors of 1154)
1154 / 2 = 577 (the remainder is 0, so 2 and 577 are divisors of 1154)
1154 / 3 = 384.66666666667 (the remainder is 2, so 3 is not a divisor of 1154)
...
1154 / 32 = 36.0625 (the remainder is 2, so 32 is not a divisor of 1154)
1154 / 33 = 34.969696969697 (the remainder is 32, so 33 is not a divisor of 1154)