What are the divisors of 1139?

1, 17, 67, 1139

There is a total of 4 positive divisors.
The sum of these divisors is 1224.
The arithmetic mean is 306.

4 odd divisors

1, 17, 67, 1139

How to compute the divisors of 1139?

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 1139 by each of the numbers from 1 to 1139 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)

1139 / 1 = 1139 (the remainder is 0, so 1 is a divisor of 1139)
1139 / 2 = 569.5 (the remainder is 1, so 2 is not a divisor of 1139)
1139 / 3 = 379.66666666667 (the remainder is 2, so 3 is not a divisor of 1139)
...
1139 / 1138 = 1.0008787346221 (the remainder is 1, so 1138 is not a divisor of 1139)
1139 / 1139 = 1 (the remainder is 0, so 1139 is a divisor of 1139)

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 1139 (i.e. 33.749074061372). 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 $\frac{N}{d} = D$ )

1139 / 1 = 1139 (the remainder is 0, so 1 and 1139 are divisors of 1139)
1139 / 2 = 569.5 (the remainder is 1, so 2 is not a divisor of 1139)
1139 / 3 = 379.66666666667 (the remainder is 2, so 3 is not a divisor of 1139)
...
1139 / 32 = 35.59375 (the remainder is 19, so 32 is not a divisor of 1139)
1139 / 33 = 34.515151515152 (the remainder is 17, so 33 is not a divisor of 1139)