WHY 1 IS NOT PRIME NO ?

If one is allowed as a prime, then any number could be written as a product of primes in many ways.

EXAMPLE.

24 = 1*2*2*2*3
or 24 = 1*1*2*2*2*3
or 24 = 1*1*1*1*1*2*2*2*3

The fact that factoring into primes can only be done in one way is important in mathematics.