Can you please help me explain why a perfect square cannot be a prime #?
Thanks!
Is it because the only numbers that can go into a prime number are "1" and itself?
Yes
a perfect square means:
perfect square = n * n
but that means it is divisible by n
Of course! I'd be happy to explain why a perfect square cannot be a prime number.
A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number is divisible only by 1 and itself.
On the other hand, a perfect square is a number that can be expressed as the square of an integer. For example, 4 is a perfect square because it can be written as 2², and 9 is a perfect square because it can be written as 3².
Now, let's consider a perfect square such as 4. If we divide it by 2, we get 2, which is a positive integer other than 1 and itself. Therefore, 4 does not meet the definition of a prime number.
Similarly, for any perfect square, its square root would be an integer. Let's take the example of 9. Its square root is 3, which is a positive integer other than 1 and 9. Thus, 9 is not a prime number either.
In general, perfect squares are not prime numbers because they have multiple divisors. Since perfect squares are always the product of two equal factors (such as 2 × 2 = 4 or 3 × 3 = 9), they can always be divided by at least two numbers other than 1 and themselves.
Therefore, a perfect square number cannot be a prime number.