Factorising 2

After the last blog there should now be now no fear of factorising. You may wonder, though, how far you can go with it. What are the smallest numbers that you can factorise a large number into? The answer is, the prime numbers. If you find any factor that isn't prime, that factor can in turn be factorised into prime numbers. Quite often you will be asked to find all the prime factors of a number.

For 28, for instance, 14 and 7 and 4 and 2 are all factors, but the 14 and the 4 are not prime. The prime factors are 7 and two 2's. Note that a single 2 is not enough, because 7 x 2 is just 14, only half of what we need. 28 has three prime factors, and it just happens that two of them are the same as each other. 28 = 7 x 2 x 2.

If I give you the question factorise 4n + 8, you need to take out the common factor. There is a common factor of 4 so factorising 4n + 8 is simple. It is 4(n + 2). I hope you followed that. I had to put a letter in the equation because that is what algebra is all about.

As long as there's just one letter, and it isn't squared or anything tricky like that, factorising is just a matter of finding the common factors, the ones that divide into both the constant part (8 in the example above) and the part which involves a variable represented by a letter (4n in the example). It can get trickier if there are squares or other powers, or if there is more than one variable, but that's a matter for another blog. Even in those cases the principle is still the same - you're trying to find simple expressions or numbers which can divide into the original expression.

That sums it up