Question

I am thinking of a number. My number is between 20 and 30 My number and 12 have only one common factor. What number could I be thinking of? Give all three possible answers.

Answer 1

21, 22 and 26

Explanation:

To answer this question first we need to know which are the factors of 12:

`12= 2^2(3)`

So, now, we need 3 numbers that are between 20 and 30 and that only have one common factor with 12, in other words, they need to have just a 2 or a 3 in their factorization.

Let's take number 21:

`21= (7)(3)`, we can see that 21 only has a 3 and a prime so therefore it has only one common factor with 12

Now, let's take the number 22,

`22=11 (2)`, thus since 22 has a 2 and a prime, it has only one common factor with 12.

Now, let's take the number 26

`26= 13 (2)`, thus, since 26 has a 2 and a prime, it has only one common factor with 12.

Thus, the three possible answers are 21, 22 and 26