Question 61095
which one of these numbers are prime and how do i show my work?
12,31,99,1

i think 1 is prime because you only have 0,1
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solution:

A prime number is a positive integer that has exactly two positive integer factors, 1 and itself.

for example, 

Facors of 2    = 1, 2
Factors of 3   = 1, 3
Factors of 4   = 1, 2, 4
Factors of 5   = 1, 5
Factors of 6   = 1, 2, 3, 6
Factors of 7   = 1, 7
Factors of 8   = 1, 2, 4, 8
Factors of 9   = 1, 3, 9
Factors of 10  = 1, 2, 5, 10

Here 2, 3, 5, 7 have factors  1  and the number  itself  only

so these anumbers are prime.


If we list the factors of 28, we have 1, 2, 4, 7, 14, and 28. That's six factors. If we list the factors of 29, we only have 1 and 29. That's two factors. So we say that 29 is a prime number, but 28 isn't.

 
Note that the definition of a prime number doesn't allow 1 to be a prime number: 1 has only one factor, namely 1. Prime numbers have exactly two factors, not "at most two" or anything like that. When a number has more than two factors it is called a composite number. 



Here are the first few prime numbers: 
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc. 



NOW LET'S COME BACK TO YOUR QUESTION.


12,31,99,1


Factors of  12 =1, 2, 3, 4, 6, 12

That means 12 has more than two factors.  So it is not a  prime.

factors of 31 = 1, 31

That means  31 has only two factors : 1 and 31(the number itself)
so 31 is a prime.

Factors of 99 = 1, 3, 33, 91
Tat means 99 has more than two factors .

So 99 is not a prime.


1  has only one  factor, namely 1. Prime numbers have exactly two factors,
So 1 is not a prime.

Additional Information:

1  is neither a prime nor a composit.

2  is only  EVEN  prime number.


BYE!!!!!!!!!!!!!!!!