What are the divisors of 4621?

1, 4621

There is a total of 2 positive divisors.
The sum of these divisors is 4622.
The arithmetic mean is 2311.

2 odd divisors

1, 4621

How to compute the divisors of 4621?

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 4621 by each of the numbers from 1 to 4621 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)

4621 / 1 = 4621 (the remainder is 0, so 1 is a divisor of 4621)
4621 / 2 = 2310.5 (the remainder is 1, so 2 is not a divisor of 4621)
4621 / 3 = 1540.3333333333 (the remainder is 1, so 3 is not a divisor of 4621)
...
4621 / 4620 = 1.0002164502165 (the remainder is 1, so 4620 is not a divisor of 4621)
4621 / 4621 = 1 (the remainder is 0, so 4621 is a divisor of 4621)

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 4621 (i.e. 67.977937597429). 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 $\frac{N}{d} = D$ )

4621 / 1 = 4621 (the remainder is 0, so 1 and 4621 are divisors of 4621)
4621 / 2 = 2310.5 (the remainder is 1, so 2 is not a divisor of 4621)
4621 / 3 = 1540.3333333333 (the remainder is 1, so 3 is not a divisor of 4621)
...
4621 / 66 = 70.015151515152 (the remainder is 1, so 66 is not a divisor of 4621)
4621 / 67 = 68.970149253731 (the remainder is 65, so 67 is not a divisor of 4621)