What are the divisors of 4222?

1, 2, 2111, 4222

There is a total of 4 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 1584.

2 even divisors

2, 4222

2 odd divisors

1, 2111

How to compute the divisors of 4222?

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 4222 by each of the numbers from 1 to 4222 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)

4222 / 1 = 4222 (the remainder is 0, so 1 is a divisor of 4222)
4222 / 2 = 2111 (the remainder is 0, so 2 is a divisor of 4222)
4222 / 3 = 1407.3333333333 (the remainder is 1, so 3 is not a divisor of 4222)
...
4222 / 4221 = 1.0002369106847 (the remainder is 1, so 4221 is not a divisor of 4222)
4222 / 4222 = 1 (the remainder is 0, so 4222 is a divisor of 4222)

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 4222 (i.e. 64.976918978973). 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 $\frac{N}{d} = D$ )

4222 / 1 = 4222 (the remainder is 0, so 1 and 4222 are divisors of 4222)
4222 / 2 = 2111 (the remainder is 0, so 2 and 2111 are divisors of 4222)
4222 / 3 = 1407.3333333333 (the remainder is 1, so 3 is not a divisor of 4222)
...
4222 / 63 = 67.015873015873 (the remainder is 1, so 63 is not a divisor of 4222)
4222 / 64 = 65.96875 (the remainder is 62, so 64 is not a divisor of 4222)