What are the divisors of 4562?

1, 2, 2281, 4562

There is a total of 4 positive divisors.
The sum of these divisors is 6846.
The arithmetic mean is 1711.5.

2 even divisors

2, 4562

2 odd divisors

1, 2281

How to compute the divisors of 4562?

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 4562 by each of the numbers from 1 to 4562 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)

4562 / 1 = 4562 (the remainder is 0, so 1 is a divisor of 4562)
4562 / 2 = 2281 (the remainder is 0, so 2 is a divisor of 4562)
4562 / 3 = 1520.6666666667 (the remainder is 2, so 3 is not a divisor of 4562)
...
4562 / 4561 = 1.0002192501644 (the remainder is 1, so 4561 is not a divisor of 4562)
4562 / 4562 = 1 (the remainder is 0, so 4562 is a divisor of 4562)

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 4562 (i.e. 67.542579163073). 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 $\frac{N}{d} = D$ )

4562 / 1 = 4562 (the remainder is 0, so 1 and 4562 are divisors of 4562)
4562 / 2 = 2281 (the remainder is 0, so 2 and 2281 are divisors of 4562)
4562 / 3 = 1520.6666666667 (the remainder is 2, so 3 is not a divisor of 4562)
...
4562 / 66 = 69.121212121212 (the remainder is 8, so 66 is not a divisor of 4562)
4562 / 67 = 68.089552238806 (the remainder is 6, so 67 is not a divisor of 4562)