What are the divisors of 6142?

1, 2, 37, 74, 83, 166, 3071, 6142

There is a total of 8 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 1197.

4 even divisors

2, 74, 166, 6142

4 odd divisors

1, 37, 83, 3071

How to compute the divisors of 6142?

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 6142 by each of the numbers from 1 to 6142 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)

6142 / 1 = 6142 (the remainder is 0, so 1 is a divisor of 6142)
6142 / 2 = 3071 (the remainder is 0, so 2 is a divisor of 6142)
6142 / 3 = 2047.3333333333 (the remainder is 1, so 3 is not a divisor of 6142)
...
6142 / 6141 = 1.0001628399284 (the remainder is 1, so 6141 is not a divisor of 6142)
6142 / 6142 = 1 (the remainder is 0, so 6142 is a divisor of 6142)

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 6142 (i.e. 78.370912971587). 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 $\frac{N}{d} = D$ )

6142 / 1 = 6142 (the remainder is 0, so 1 and 6142 are divisors of 6142)
6142 / 2 = 3071 (the remainder is 0, so 2 and 3071 are divisors of 6142)
6142 / 3 = 2047.3333333333 (the remainder is 1, so 3 is not a divisor of 6142)
...
6142 / 77 = 79.766233766234 (the remainder is 59, so 77 is not a divisor of 6142)
6142 / 78 = 78.74358974359 (the remainder is 58, so 78 is not a divisor of 6142)