How To Find The Highest Common Factor

Hi, I'm Rebecca, and in this film we're going to look at how to find the highest common factor of two numbers. Now, a factor of a number is a number that divides into it exactly with no remainder. And two numbers that multiply together to make a number are known as factor pairs. So let's have a look at the factors of 12. Well, the factor pairs that make 12 are 1 and 12, 2 and 6 and 3 and 4. Now, here I also have the factors of 30, and you can see that some of them are common. They both have 1 and 2 and 3 and 6 as factors. So we can say that the highest common factor of 12 and 30 is 6. Finding the highest common factor is essential when you're simplifying fractions. Here I'm asked, what is 1842ths in its simplest form? So I've written out the factors of 18 and the factors of 42. And here again, we can see that we have some common factors. We have 1 and 2 and 3 and 6 is the highest common factor. So to simplify, I need to divide the numerator and the denominator by 6. 18 divided by 6 is 3 and 42 divided by 6 is 7. So I now, in its simplest form, have a fraction of 3/7. So why are we finding the highest common factor? Why not just any factor? Well, if you divide by a larger number, you're going to get a smaller answer. So we know that we've got the fraction written in its simplest form. So there you go. That's how to find the highest common factor of two numbers.