What are the divisors of 4677?

1, 3, 1559, 4677

There is a total of 4 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 1560.

4 odd divisors

1, 3, 1559, 4677

How to compute the divisors of 4677?

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 4677 by each of the numbers from 1 to 4677 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)

4677 / 1 = 4677 (the remainder is 0, so 1 is a divisor of 4677)
4677 / 2 = 2338.5 (the remainder is 1, so 2 is not a divisor of 4677)
4677 / 3 = 1559 (the remainder is 0, so 3 is a divisor of 4677)
...
4677 / 4676 = 1.0002138579983 (the remainder is 1, so 4676 is not a divisor of 4677)
4677 / 4677 = 1 (the remainder is 0, so 4677 is a divisor of 4677)

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 4677 (i.e. 68.388595540485). 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 $\frac{N}{d} = D$ )

4677 / 1 = 4677 (the remainder is 0, so 1 and 4677 are divisors of 4677)
4677 / 2 = 2338.5 (the remainder is 1, so 2 is not a divisor of 4677)
4677 / 3 = 1559 (the remainder is 0, so 3 and 1559 are divisors of 4677)
...
4677 / 67 = 69.805970149254 (the remainder is 54, so 67 is not a divisor of 4677)
4677 / 68 = 68.779411764706 (the remainder is 53, so 68 is not a divisor of 4677)