What are the divisors of 4746?

1, 2, 3, 6, 7, 14, 21, 42, 113, 226, 339, 678, 791, 1582, 2373, 4746

There is a total of 16 positive divisors.
The sum of these divisors is 10944.
The arithmetic mean is 684.

8 even divisors

2, 6, 14, 42, 226, 678, 1582, 4746

8 odd divisors

1, 3, 7, 21, 113, 339, 791, 2373

How to compute the divisors of 4746?

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 4746 by each of the numbers from 1 to 4746 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)

4746 / 1 = 4746 (the remainder is 0, so 1 is a divisor of 4746)
4746 / 2 = 2373 (the remainder is 0, so 2 is a divisor of 4746)
4746 / 3 = 1582 (the remainder is 0, so 3 is a divisor of 4746)
...
4746 / 4745 = 1.000210748156 (the remainder is 1, so 4745 is not a divisor of 4746)
4746 / 4746 = 1 (the remainder is 0, so 4746 is a divisor of 4746)

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 4746 (i.e. 68.891218598599). 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 $\frac{N}{d} = D$ )

4746 / 1 = 4746 (the remainder is 0, so 1 and 4746 are divisors of 4746)
4746 / 2 = 2373 (the remainder is 0, so 2 and 2373 are divisors of 4746)
4746 / 3 = 1582 (the remainder is 0, so 3 and 1582 are divisors of 4746)
...
4746 / 67 = 70.835820895522 (the remainder is 56, so 67 is not a divisor of 4746)
4746 / 68 = 69.794117647059 (the remainder is 54, so 68 is not a divisor of 4746)