What are the divisors of 4738?

1, 2, 23, 46, 103, 206, 2369, 4738

There is a total of 8 positive divisors.
The sum of these divisors is 7488.
The arithmetic mean is 936.

4 even divisors

2, 46, 206, 4738

4 odd divisors

1, 23, 103, 2369

How to compute the divisors of 4738?

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 4738 by each of the numbers from 1 to 4738 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)

4738 / 1 = 4738 (the remainder is 0, so 1 is a divisor of 4738)
4738 / 2 = 2369 (the remainder is 0, so 2 is a divisor of 4738)
4738 / 3 = 1579.3333333333 (the remainder is 1, so 3 is not a divisor of 4738)
...
4738 / 4737 = 1.0002111040743 (the remainder is 1, so 4737 is not a divisor of 4738)
4738 / 4738 = 1 (the remainder is 0, so 4738 is a divisor of 4738)

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 4738 (i.e. 68.833131557412). 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 $\frac{N}{d} = D$ )

4738 / 1 = 4738 (the remainder is 0, so 1 and 4738 are divisors of 4738)
4738 / 2 = 2369 (the remainder is 0, so 2 and 2369 are divisors of 4738)
4738 / 3 = 1579.3333333333 (the remainder is 1, so 3 is not a divisor of 4738)
...
4738 / 67 = 70.716417910448 (the remainder is 48, so 67 is not a divisor of 4738)
4738 / 68 = 69.676470588235 (the remainder is 46, so 68 is not a divisor of 4738)