What are the divisors of 4627?

1, 7, 661, 4627

There is a total of 4 positive divisors.
The sum of these divisors is 5296.
The arithmetic mean is 1324.

4 odd divisors

1, 7, 661, 4627

How to compute the divisors of 4627?

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 4627 by each of the numbers from 1 to 4627 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)

4627 / 1 = 4627 (the remainder is 0, so 1 is a divisor of 4627)
4627 / 2 = 2313.5 (the remainder is 1, so 2 is not a divisor of 4627)
4627 / 3 = 1542.3333333333 (the remainder is 1, so 3 is not a divisor of 4627)
...
4627 / 4626 = 1.0002161694769 (the remainder is 1, so 4626 is not a divisor of 4627)
4627 / 4627 = 1 (the remainder is 0, so 4627 is a divisor of 4627)

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 4627 (i.e. 68.022055246809). 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 $\frac{N}{d} = D$ )

4627 / 1 = 4627 (the remainder is 0, so 1 and 4627 are divisors of 4627)
4627 / 2 = 2313.5 (the remainder is 1, so 2 is not a divisor of 4627)
4627 / 3 = 1542.3333333333 (the remainder is 1, so 3 is not a divisor of 4627)
...
4627 / 67 = 69.059701492537 (the remainder is 4, so 67 is not a divisor of 4627)
4627 / 68 = 68.044117647059 (the remainder is 3, so 68 is not a divisor of 4627)