Knowing The Math - Prime Factorisation Method for finding the Highest Common Factor

There are many ways which we can find the HCF of 2 numbers, but in this post we will look at the prime factor method

We want to find the HCF of 24 and 36 what we need to do is very simple, we just have to reduce the numbers to it prime factors first

We can do that using upside down division.

Let's find the prime factors of 24 we draw two lines like in the image

Now we think of all the prime factors 24 is divisible by we start with 2, 24 is divisible by 2 so we write 2

2 times 12 is 24,

And 12 is also divisible by 2 yes 12 is also divisible by 2 we write 2 again and draw a line

2 times 6 is 12

6 is also divisible by 2

And 2 times 3 is 6 we stop here since we got a prime factor

24 can be written as 2 multiplied by 2 multiplied by 2 multiplied by 3 we've reduced 24 to its prime factors

We do the same For 36, 36 is divisible by 2

And 2 times 18 is 36

18 is divisible by 2

And 2 times 9 is 18, 9 is not divisible by 2 hence we jump to the next prime number It is 3

And 9 is divisible by 3, yes, 3 times 3 is 9

We stop here since it's a prime factor

36 can be written as the product of the numbers you see in the image

36 is equal to 2 multiplied by 2 multiplied by 3 multiplied by 3 the difficult part is over

To find the HCF all we have to do is multiplied the prime factors that the common to both the numbers 2 is common to both so we write 2

There is another 2 that is common to both so we multiply this 2 with another 2

And there is a 3 which is common to both the numbers, hence we multiply the product of 2 times 2 product with 3

2 times 2 is 4 and 4 times 3 is 12 the highest common factor of 24 and 36 is 12

This method is better than trying to write each number as a product of two numbers to finding the highest common factor.

Thank you for your attention!