What are the divisors of 4742?

1, 2, 2371, 4742

There is a total of 4 positive divisors.
The sum of these divisors is 7116.
The arithmetic mean is 1779.

2 even divisors

2, 4742

2 odd divisors

1, 2371

How to compute the divisors of 4742?

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 4742 by each of the numbers from 1 to 4742 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)

4742 / 1 = 4742 (the remainder is 0, so 1 is a divisor of 4742)
4742 / 2 = 2371 (the remainder is 0, so 2 is a divisor of 4742)
4742 / 3 = 1580.6666666667 (the remainder is 2, so 3 is not a divisor of 4742)
...
4742 / 4741 = 1.000210925965 (the remainder is 1, so 4741 is not a divisor of 4742)
4742 / 4742 = 1 (the remainder is 0, so 4742 is a divisor of 4742)

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 4742 (i.e. 68.862181202747). 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 $\frac{N}{d} = D$ )

4742 / 1 = 4742 (the remainder is 0, so 1 and 4742 are divisors of 4742)
4742 / 2 = 2371 (the remainder is 0, so 2 and 2371 are divisors of 4742)
4742 / 3 = 1580.6666666667 (the remainder is 2, so 3 is not a divisor of 4742)
...
4742 / 67 = 70.776119402985 (the remainder is 52, so 67 is not a divisor of 4742)
4742 / 68 = 69.735294117647 (the remainder is 50, so 68 is not a divisor of 4742)