Question 163303: If a number is the square of a prime number, it has exactly 3 divisors. Give an example and explain.
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source):
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
If a number is the square of a prime number, it has
exactly 3 divisors. Give an example and explain.
Take the prime number 2. Square it. Get 4. 4
has exactly three divisors. They are 1, 2 and 4,
because all three of those but no others will divide
evenly into 4.
Take the prime number 3. Square it. Get 9. 9 has
exactly three divisors. They are 1, 3 and 9, because
all three of those but no others will divide evenly into 9.
Take the prime number 5. Square it. Get 25. 25 has
exactly three divisors. They are 1, 5 and 25, because all
three of those but no others will divide evenly into 25.
Take the prime number 11. Square it. Get 121. 121
has exactly three divisors. They are 1, 11 and 121, because
all three of those but no others will divide evenly into 11.
----
Now, to elaborate, you might wonder if that would work if
you started with a number other than a prime number. The
answer is no, but we need to demonstrate this:
Take the non-prime number 4. Square it. Get 16. But 16
has FIVE divisors. They are 1,2,4,8,16. because all FIVE of
those but no others will divide evenly into 16.
So it doesn't work for square of the non-prime 4.
Take the non-prime number 1. Square it. Get 1. But 1
has only ONE divisor. That is 1 itself. because that is the
only number that will divide evenly into 1.
So it doesn't work for the square of the non-prime 1 either.
Edwin
|
|
|
