What are the divisors of 3142?

1, 2, 1571, 3142

There is a total of 4 positive divisors.
The sum of these divisors is 4716.
The arithmetic mean is 1179.

2 even divisors

2, 3142

2 odd divisors

1, 1571

How to compute the divisors of 3142?

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 3142 by each of the numbers from 1 to 3142 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)

3142 / 1 = 3142 (the remainder is 0, so 1 is a divisor of 3142)
3142 / 2 = 1571 (the remainder is 0, so 2 is a divisor of 3142)
3142 / 3 = 1047.3333333333 (the remainder is 1, so 3 is not a divisor of 3142)
...
3142 / 3141 = 1.0003183699459 (the remainder is 1, so 3141 is not a divisor of 3142)
3142 / 3142 = 1 (the remainder is 0, so 3142 is a divisor of 3142)

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 3142 (i.e. 56.053545828966). 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 $\frac{N}{d} = D$ )

3142 / 1 = 3142 (the remainder is 0, so 1 and 3142 are divisors of 3142)
3142 / 2 = 1571 (the remainder is 0, so 2 and 1571 are divisors of 3142)
3142 / 3 = 1047.3333333333 (the remainder is 1, so 3 is not a divisor of 3142)
...
3142 / 55 = 57.127272727273 (the remainder is 7, so 55 is not a divisor of 3142)
3142 / 56 = 56.107142857143 (the remainder is 6, so 56 is not a divisor of 3142)