What are the divisors of 4210?

1, 2, 5, 10, 421, 842, 2105, 4210

There is a total of 8 positive divisors.
The sum of these divisors is 7596.
The arithmetic mean is 949.5.

4 even divisors

2, 10, 842, 4210

4 odd divisors

1, 5, 421, 2105

How to compute the divisors of 4210?

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 4210 by each of the numbers from 1 to 4210 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)

4210 / 1 = 4210 (the remainder is 0, so 1 is a divisor of 4210)
4210 / 2 = 2105 (the remainder is 0, so 2 is a divisor of 4210)
4210 / 3 = 1403.3333333333 (the remainder is 1, so 3 is not a divisor of 4210)
...
4210 / 4209 = 1.000237586125 (the remainder is 1, so 4209 is not a divisor of 4210)
4210 / 4210 = 1 (the remainder is 0, so 4210 is a divisor of 4210)

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 4210 (i.e. 64.884512790033). 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 $\frac{N}{d} = D$ )

4210 / 1 = 4210 (the remainder is 0, so 1 and 4210 are divisors of 4210)
4210 / 2 = 2105 (the remainder is 0, so 2 and 2105 are divisors of 4210)
4210 / 3 = 1403.3333333333 (the remainder is 1, so 3 is not a divisor of 4210)
...
4210 / 63 = 66.825396825397 (the remainder is 52, so 63 is not a divisor of 4210)
4210 / 64 = 65.78125 (the remainder is 50, so 64 is not a divisor of 4210)