What are the divisors of 4242?

1, 2, 3, 6, 7, 14, 21, 42, 101, 202, 303, 606, 707, 1414, 2121, 4242

There is a total of 16 positive divisors.
The sum of these divisors is 9792.
The arithmetic mean is 612.

8 even divisors

2, 6, 14, 42, 202, 606, 1414, 4242

8 odd divisors

1, 3, 7, 21, 101, 303, 707, 2121

How to compute the divisors of 4242?

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 4242 by each of the numbers from 1 to 4242 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)

4242 / 1 = 4242 (the remainder is 0, so 1 is a divisor of 4242)
4242 / 2 = 2121 (the remainder is 0, so 2 is a divisor of 4242)
4242 / 3 = 1414 (the remainder is 0, so 3 is a divisor of 4242)
...
4242 / 4241 = 1.0002357934449 (the remainder is 1, so 4241 is not a divisor of 4242)
4242 / 4242 = 1 (the remainder is 0, so 4242 is a divisor of 4242)

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 4242 (i.e. 65.130637951735). 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 $\frac{N}{d} = D$ )

4242 / 1 = 4242 (the remainder is 0, so 1 and 4242 are divisors of 4242)
4242 / 2 = 2121 (the remainder is 0, so 2 and 2121 are divisors of 4242)
4242 / 3 = 1414 (the remainder is 0, so 3 and 1414 are divisors of 4242)
...
4242 / 64 = 66.28125 (the remainder is 18, so 64 is not a divisor of 4242)
4242 / 65 = 65.261538461538 (the remainder is 17, so 65 is not a divisor of 4242)