hoofclid:

I think if I try to draw an answer to this one my hand will fall off. Besides, Braeburn is twirling his lasso again. So text it is!

One reason that comes up more often than you might think is the following theorem, sometimes called the ‘Fundamental Theorem of Arithmetic” by people who like to give things over-dramatic names. 

Theorem. Every positive whole number can be written as a product of prime numbers in a unique way.

So for instance 42 = 2x3x7 and there’s no other way to write this as a product of primes. That simply isn’t true if you allow 1 to be a prime- 42= 1x2x3x7=1x1x2x3x7….

That’s just one example, but as I say it crops up a lot. 

Thanks! That actually sounds familiar! I think I heard that before but had never committed it to memory.