What are the divisors of 1142?

1, 2, 571, 1142

There is a total of 4 positive divisors.
The sum of these divisors is 1716.
The arithmetic mean is 429.

2 even divisors

2, 1142

2 odd divisors

1, 571

How to compute the divisors of 1142?

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 1142 by each of the numbers from 1 to 1142 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)

1142 / 1 = 1142 (the remainder is 0, so 1 is a divisor of 1142)
1142 / 2 = 571 (the remainder is 0, so 2 is a divisor of 1142)
1142 / 3 = 380.66666666667 (the remainder is 2, so 3 is not a divisor of 1142)
...
1142 / 1141 = 1.0008764241893 (the remainder is 1, so 1141 is not a divisor of 1142)
1142 / 1142 = 1 (the remainder is 0, so 1142 is a divisor of 1142)

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 1142 (i.e. 33.793490497432). 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 $\frac{N}{d} = D$ )

1142 / 1 = 1142 (the remainder is 0, so 1 and 1142 are divisors of 1142)
1142 / 2 = 571 (the remainder is 0, so 2 and 571 are divisors of 1142)
1142 / 3 = 380.66666666667 (the remainder is 2, so 3 is not a divisor of 1142)
...
1142 / 32 = 35.6875 (the remainder is 22, so 32 is not a divisor of 1142)
1142 / 33 = 34.606060606061 (the remainder is 20, so 33 is not a divisor of 1142)