What are the divisors of 4202?

1, 2, 11, 22, 191, 382, 2101, 4202

There is a total of 8 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 864.

4 even divisors

2, 22, 382, 4202

4 odd divisors

1, 11, 191, 2101

How to compute the divisors of 4202?

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 4202 by each of the numbers from 1 to 4202 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)

4202 / 1 = 4202 (the remainder is 0, so 1 is a divisor of 4202)
4202 / 2 = 2101 (the remainder is 0, so 2 is a divisor of 4202)
4202 / 3 = 1400.6666666667 (the remainder is 2, so 3 is not a divisor of 4202)
...
4202 / 4201 = 1.0002380385622 (the remainder is 1, so 4201 is not a divisor of 4202)
4202 / 4202 = 1 (the remainder is 0, so 4202 is a divisor of 4202)

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 4202 (i.e. 64.822835482567). 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 $\frac{N}{d} = D$ )

4202 / 1 = 4202 (the remainder is 0, so 1 and 4202 are divisors of 4202)
4202 / 2 = 2101 (the remainder is 0, so 2 and 2101 are divisors of 4202)
4202 / 3 = 1400.6666666667 (the remainder is 2, so 3 is not a divisor of 4202)
...
4202 / 63 = 66.698412698413 (the remainder is 44, so 63 is not a divisor of 4202)
4202 / 64 = 65.65625 (the remainder is 42, so 64 is not a divisor of 4202)