Product of Prime Factors

Question
Express 240 as a product of prime factors

This question couldn't be easier! It just requires you to understand a few simple things:

- factors are the numbers that will divide a number exactly
e.g. the factors of 8 are 1, 2, 4, and 8, as these are the numbers that divide 8 exactly
       the factors of 35 are 1, 5, 7, 35

- prime numbers are numbers that have only two factors: 1 and itself
e.g. 7 is a prime number, because its factors are 1 and 7
      11 is a prime number, because its factors are 1 and 11
      1 is not a prime number as it has only one factor

- a product is a multiplication
e.g. 2 x 3 is a product
       7 x 11 x 13 is a product

Solution
We must split 240 up into a product of prime factors.
- Choose prime numbers that go into 240 to form a factor tree, as shown below. 
- Start by seeing if 2 goes into 240, and keep doing this until it no longer divides the number you get. 
- Then try 3, then 5, 7, 11, 13, etc. (the prime numbers). 
- Stop when you get to a prime number.

                240
               /      \
             2      120                     (240 = 2 x 120)
                    /      \
                  2       60                 (120 = 2 x 60)
                         /      \
                       2       30            (60 = 30 x 2)
                              /      \
                            2       15       (30 = 2 x 15)
                                   /      \
                                 3        5

We can express 240 as a product of the prime factors from our tree (2, 2, 2, 2, 3, 5)

Answer: 240 = 2 x 2 x 2 x 2 x 3 x 5

Remember: The solution is not complete unless you write "240 = 2 x 2 x 2 x 2 x 3 x 5", as this is the product of prime factors. You will lose marks if you do not finish the question in this way.

Top Tip: Practise this question with lots of different numbers (you choose!), and you're bound to get it right in the exam.


Don't forget you can email your maths questions to mathshints@gmail.com, and follow us on Twitter!