What are the divisors of 4213?

1, 11, 383, 4213

There is a total of 4 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 1152.

4 odd divisors

1, 11, 383, 4213

How to compute the divisors of 4213?

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 4213 by each of the numbers from 1 to 4213 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)

4213 / 1 = 4213 (the remainder is 0, so 1 is a divisor of 4213)
4213 / 2 = 2106.5 (the remainder is 1, so 2 is not a divisor of 4213)
4213 / 3 = 1404.3333333333 (the remainder is 1, so 3 is not a divisor of 4213)
...
4213 / 4212 = 1.0002374169041 (the remainder is 1, so 4212 is not a divisor of 4213)
4213 / 4213 = 1 (the remainder is 0, so 4213 is a divisor of 4213)

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 4213 (i.e. 64.907626670523). 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 $\frac{N}{d} = D$ )

4213 / 1 = 4213 (the remainder is 0, so 1 and 4213 are divisors of 4213)
4213 / 2 = 2106.5 (the remainder is 1, so 2 is not a divisor of 4213)
4213 / 3 = 1404.3333333333 (the remainder is 1, so 3 is not a divisor of 4213)
...
4213 / 63 = 66.873015873016 (the remainder is 55, so 63 is not a divisor of 4213)
4213 / 64 = 65.828125 (the remainder is 53, so 64 is not a divisor of 4213)