What are the divisors of 4737?

1, 3, 1579, 4737

There is a total of 4 positive divisors.
The sum of these divisors is 6320.
The arithmetic mean is 1580.

4 odd divisors

1, 3, 1579, 4737

How to compute the divisors of 4737?

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 4737 by each of the numbers from 1 to 4737 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)

4737 / 1 = 4737 (the remainder is 0, so 1 is a divisor of 4737)
4737 / 2 = 2368.5 (the remainder is 1, so 2 is not a divisor of 4737)
4737 / 3 = 1579 (the remainder is 0, so 3 is a divisor of 4737)
...
4737 / 4736 = 1.0002111486486 (the remainder is 1, so 4736 is not a divisor of 4737)
4737 / 4737 = 1 (the remainder is 0, so 4737 is a divisor of 4737)

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 4737 (i.e. 68.825867230279). 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 $\frac{N}{d} = D$ )

4737 / 1 = 4737 (the remainder is 0, so 1 and 4737 are divisors of 4737)
4737 / 2 = 2368.5 (the remainder is 1, so 2 is not a divisor of 4737)
4737 / 3 = 1579 (the remainder is 0, so 3 and 1579 are divisors of 4737)
...
4737 / 67 = 70.701492537313 (the remainder is 47, so 67 is not a divisor of 4737)
4737 / 68 = 69.661764705882 (the remainder is 45, so 68 is not a divisor of 4737)