What are the divisors of 1242?

1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 69, 138, 207, 414, 621, 1242

There is a total of 16 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 180.

8 even divisors

2, 6, 18, 46, 54, 138, 414, 1242

8 odd divisors

1, 3, 9, 23, 27, 69, 207, 621

How to compute the divisors of 1242?

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 1242 by each of the numbers from 1 to 1242 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)

1242 / 1 = 1242 (the remainder is 0, so 1 is a divisor of 1242)
1242 / 2 = 621 (the remainder is 0, so 2 is a divisor of 1242)
1242 / 3 = 414 (the remainder is 0, so 3 is a divisor of 1242)
...
1242 / 1241 = 1.0008058017728 (the remainder is 1, so 1241 is not a divisor of 1242)
1242 / 1242 = 1 (the remainder is 0, so 1242 is a divisor of 1242)

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 1242 (i.e. 35.242020373412). 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 $\frac{N}{d} = D$ )

1242 / 1 = 1242 (the remainder is 0, so 1 and 1242 are divisors of 1242)
1242 / 2 = 621 (the remainder is 0, so 2 and 621 are divisors of 1242)
1242 / 3 = 414 (the remainder is 0, so 3 and 414 are divisors of 1242)
...
1242 / 34 = 36.529411764706 (the remainder is 18, so 34 is not a divisor of 1242)
1242 / 35 = 35.485714285714 (the remainder is 17, so 35 is not a divisor of 1242)