What are the divisors of 4749?

1, 3, 1583, 4749

There is a total of 4 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 1584.

4 odd divisors

1, 3, 1583, 4749

How to compute the divisors of 4749?

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 4749 by each of the numbers from 1 to 4749 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)

4749 / 1 = 4749 (the remainder is 0, so 1 is a divisor of 4749)
4749 / 2 = 2374.5 (the remainder is 1, so 2 is not a divisor of 4749)
4749 / 3 = 1583 (the remainder is 0, so 3 is a divisor of 4749)
...
4749 / 4748 = 1.0002106149958 (the remainder is 1, so 4748 is not a divisor of 4749)
4749 / 4749 = 1 (the remainder is 0, so 4749 is a divisor of 4749)

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 4749 (i.e. 68.91298861608). 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 $\frac{N}{d} = D$ )

4749 / 1 = 4749 (the remainder is 0, so 1 and 4749 are divisors of 4749)
4749 / 2 = 2374.5 (the remainder is 1, so 2 is not a divisor of 4749)
4749 / 3 = 1583 (the remainder is 0, so 3 and 1583 are divisors of 4749)
...
4749 / 67 = 70.880597014925 (the remainder is 59, so 67 is not a divisor of 4749)
4749 / 68 = 69.838235294118 (the remainder is 57, so 68 is not a divisor of 4749)