Being able to find the prime factors of a number is very useful in many different ways, and this is exactly what the FACT key on your calculator does.
To find the prime factors of 56 we enter 56 (press the = key of course to enter it) then the shift key then the FACT key.
Do remember that in an exam finding the factors of a number may be in the non-calculator paper so do make certain you can do this without a calculator: you can find the instructions here.
If the number you enter is prime you just get the number back, try it for yourself.
In what follows I have used a table of the first five hundred prime numbers, downloaded from the internet - I am not really as clever as I pretend.
If you try to factorise 726403 you will get the answer 991 × 733 but it will take a time; if you try 11299331 you will, eventually, get the same number but in brackets, meaning your calculator has given up trying. (The answer is 3191 × 3541 if you want to know.)
You can of course get factorisation programs for laptops, PCs and mainframes capable of factorising much larger numbers. If we multiply two very large prime numbers together, say one hundred digits each, finding the factors of the answer would take a mainframe several hours, if the primes were each a thousand digits it would take the World’s most powerful computers several months, make it a million digits and it would be not impossible but what mathematicians call computationally infeasible. Million digit primes really do exist, and some ways of encrypting data are based upon this. This is discussed on another Page (under construction).
