i am thinking of a number between 20 and 50. it is an even number. it has exactly 9 factors. what is the number?
If it has exactly 9 factors, it must be a perfect square, as only perfect squares have an odd number of factors (including 1 and the number itself).
Between 20 and 50, there are 3 perfect squares, only one of which has more than three factors.
Post if further help is required.
tell me
is it 34
To find the number, we need to consider the two given conditions: it is an even number and it has exactly 9 factors.
First, let's identify the even numbers between 20 and 50: 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, and 50.
Now, we need to determine which of these numbers have exactly 9 factors. To do this, we can list the factors of each number and count how many there are.
Let's start with 20:
Factors: 1, 2, 4, 5, 10, 20
Count: 6 (not 9)
Next, 22:
Factors: 1, 2, 11, 22
Count: 4 (not 9)
We continue this process for each remaining number until we find the one with exactly 9 factors.
Now, let's check 24:
Factors: 1, 2, 3, 4, 6, 8, 12, 24
Count: 8 (not 9)
Next, 26:
Factors: 1, 2, 13, 26
Count: 4 (not 9)
Continuing this process, we find that the number 42 has exactly 9 factors.
Factors: 1, 2, 3, 6, 7, 14, 21, 42
Count: 8 (9 factors)
Therefore, the number you are thinking of is 42.