How do I write a number as a product of its prime factors?

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I find that the easiest way to do these questions is to use a factor tree. Starting with your original value, divide the largest number into smaller chunks. Once you are left with only prime numbers remaining (because you can divide prime numbers), count how many of each prime number you have and present them like I do under the example below. So if we were asked to write 72 as a product of its prime factors, it would look something like this.

72

2 x 36

      2 x 18

            2 x 9

                  3 x 3

This leaves you with 3 2s and 2 3s which makes your answer, 2^3 x 3^2. An important thing to remember is that the order that you divide the numbers by doesn't matter. You will always end up with the same result. For example.

72

3 x 24

      2 x 12

            3 x 4

                  2 x 2

If you count the primes we have 2 3s and 3 2s, giving us an answer of 2^3 x 3^2. You see, no matter the order that you divide by, the answer remains exactly the same!

Thomas H. A Level Maths tutor, IB Maths tutor, 13 plus  Maths tutor, ...

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