I love factorising numbers into prime factors, or as a mathematical friend of mine calls it, smashing numbers. I was first shown it as a student, when a mathematician used it to explain to me what a prime number is, and how fundamental they are to mathematics.
You have to understand that I come from a generation whose mathematical education consisted of sitting down and opening the textbook to yesterday’s page and carrying on, so my knowledge, even as a teenager, was pretty meagre.
For anyone who hasn’t done it, here goes:
Pick a number, for instance 32. Write it down and, below it, draw two lines to form an upside-down V. At the base of each line, give two factors of the starting number. For 32, you might have 2 and 16.
Now, whenever you reach a prime number, put a ring around it and stop. You can’t carry on factorising a prime, after all. If the end of a branch isn’t a prime, carry on factorising until all branches end in a prime. So, 2 would be circled, while 16 wouldn’t. Leave 2 alone, but continue to factorise 16 into 4 and 4, then 2 and 2 and 2 and 2.
You should have a list of circled prime numbers. Now, multiply them all together, and what do you get? The starting number, of course.
Try factorising the same number in two different ways. You end up with different intermediate numbers, but the final primes at the tips of the ‘roots’ are, if course, identical.
Have a go a factorising two numbers, then multiplying all the prime factors together. The children will find that they get the product of the two starting numbers.
I think I’m easily pleased, but this still blows my mind every time I do it. Primes are the roots of all the numbers in the world, and the more the children delve into the subject, the more they will learn about the fundamentals of maths.
