What are the divisors of 4763?

1, 11, 433, 4763

There is a total of 4 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 1302.

4 odd divisors

1, 11, 433, 4763

How to compute the divisors of 4763?

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 4763 by each of the numbers from 1 to 4763 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)

4763 / 1 = 4763 (the remainder is 0, so 1 is a divisor of 4763)
4763 / 2 = 2381.5 (the remainder is 1, so 2 is not a divisor of 4763)
4763 / 3 = 1587.6666666667 (the remainder is 2, so 3 is not a divisor of 4763)
...
4763 / 4762 = 1.0002099958001 (the remainder is 1, so 4762 is not a divisor of 4763)
4763 / 4763 = 1 (the remainder is 0, so 4763 is a divisor of 4763)

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 4763 (i.e. 69.014491231914). 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 $\frac{N}{d} = D$ )

4763 / 1 = 4763 (the remainder is 0, so 1 and 4763 are divisors of 4763)
4763 / 2 = 2381.5 (the remainder is 1, so 2 is not a divisor of 4763)
4763 / 3 = 1587.6666666667 (the remainder is 2, so 3 is not a divisor of 4763)
...
4763 / 68 = 70.044117647059 (the remainder is 3, so 68 is not a divisor of 4763)
4763 / 69 = 69.028985507246 (the remainder is 2, so 69 is not a divisor of 4763)