What are the divisors of 4421?

1, 4421

There is a total of 2 positive divisors.
The sum of these divisors is 4422.
The arithmetic mean is 2211.

2 odd divisors

1, 4421

How to compute the divisors of 4421?

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 4421 by each of the numbers from 1 to 4421 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)

4421 / 1 = 4421 (the remainder is 0, so 1 is a divisor of 4421)
4421 / 2 = 2210.5 (the remainder is 1, so 2 is not a divisor of 4421)
4421 / 3 = 1473.6666666667 (the remainder is 2, so 3 is not a divisor of 4421)
...
4421 / 4420 = 1.0002262443439 (the remainder is 1, so 4420 is not a divisor of 4421)
4421 / 4421 = 1 (the remainder is 0, so 4421 is a divisor of 4421)

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 4421 (i.e. 66.490600839517). 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 $\frac{N}{d} = D$ )

4421 / 1 = 4421 (the remainder is 0, so 1 and 4421 are divisors of 4421)
4421 / 2 = 2210.5 (the remainder is 1, so 2 is not a divisor of 4421)
4421 / 3 = 1473.6666666667 (the remainder is 2, so 3 is not a divisor of 4421)
...
4421 / 65 = 68.015384615385 (the remainder is 1, so 65 is not a divisor of 4421)
4421 / 66 = 66.984848484848 (the remainder is 65, so 66 is not a divisor of 4421)