Number 1 – Prime or Not

The Number 1 – is it a prime number?

So – we normally say, a prime number is a number that can only be divided by itself and 1. A good working definition that most children know, understand and readily accept. But …

… but 1 is not a prime number.

Why? Well, the true definition of a prime number is “a number that has 2, and exactly 2, factors”

For example, the factors of 13 are: 1 and 13, the factors of 7: 1 and 7, the factors of 29: 1 and 29 etc.  All are prime numbers. All have exactly 2 factors.

But the factors of 1 are … just 1. So the number 1 has only one factor, so its not a prime number.

In fact, its interesting that most numbers have an even number of factors, but 1 (and some others, say 4, 81, 49 100 amongst others) has an odd number of factors.

I wonder why that is ? !