What are the divisors of 4762?

1, 2, 2381, 4762

There is a total of 4 positive divisors.
The sum of these divisors is 7146.
The arithmetic mean is 1786.5.

2 even divisors

2, 4762

2 odd divisors

1, 2381

How to compute the divisors of 4762?

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 4762 by each of the numbers from 1 to 4762 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)

4762 / 1 = 4762 (the remainder is 0, so 1 is a divisor of 4762)
4762 / 2 = 2381 (the remainder is 0, so 2 is a divisor of 4762)
4762 / 3 = 1587.3333333333 (the remainder is 1, so 3 is not a divisor of 4762)
...
4762 / 4761 = 1.0002100399076 (the remainder is 1, so 4761 is not a divisor of 4762)
4762 / 4762 = 1 (the remainder is 0, so 4762 is a divisor of 4762)

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 4762 (i.e. 69.007245996344). 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 $\frac{N}{d} = D$ )

4762 / 1 = 4762 (the remainder is 0, so 1 and 4762 are divisors of 4762)
4762 / 2 = 2381 (the remainder is 0, so 2 and 2381 are divisors of 4762)
4762 / 3 = 1587.3333333333 (the remainder is 1, so 3 is not a divisor of 4762)
...
4762 / 68 = 70.029411764706 (the remainder is 2, so 68 is not a divisor of 4762)
4762 / 69 = 69.014492753623 (the remainder is 1, so 69 is not a divisor of 4762)