What are the divisors of 4629?

1, 3, 1543, 4629

There is a total of 4 positive divisors.
The sum of these divisors is 6176.
The arithmetic mean is 1544.

4 odd divisors

1, 3, 1543, 4629

How to compute the divisors of 4629?

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 4629 by each of the numbers from 1 to 4629 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)

4629 / 1 = 4629 (the remainder is 0, so 1 is a divisor of 4629)
4629 / 2 = 2314.5 (the remainder is 1, so 2 is not a divisor of 4629)
4629 / 3 = 1543 (the remainder is 0, so 3 is a divisor of 4629)
...
4629 / 4628 = 1.0002160760588 (the remainder is 1, so 4628 is not a divisor of 4629)
4629 / 4629 = 1 (the remainder is 0, so 4629 is a divisor of 4629)

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 4629 (i.e. 68.036754772696). 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 $\frac{N}{d} = D$ )

4629 / 1 = 4629 (the remainder is 0, so 1 and 4629 are divisors of 4629)
4629 / 2 = 2314.5 (the remainder is 1, so 2 is not a divisor of 4629)
4629 / 3 = 1543 (the remainder is 0, so 3 and 1543 are divisors of 4629)
...
4629 / 67 = 69.089552238806 (the remainder is 6, so 67 is not a divisor of 4629)
4629 / 68 = 68.073529411765 (the remainder is 5, so 68 is not a divisor of 4629)