Asked by EmmaMaths ๐Ÿ’ฏ

Express 24 as a product of prime factors?

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Ethan Lee

Recently completed an MSc in Mathematics, with teaching experience and training.

To answer questions like this, there are two stages. First, you should write down a list of the first 6 or 7 prime numbers. These prime numbers are 2,3,5,7,11,13,17. To find the prime factorisation of 24, check if 2 divides into 24. It does, because 24=12*2. Repeat this check for 12 now (here 12 is called the quotient). 2 does divide 12 because 12=6*2. Repeat this check for 6 now. 2 does divide 6 because 6=3*2. This is a prime factorisation because 2 and 3 are in the list. Therefore, by substituting all of these factorisations, 24=12*2=6*2*2=3*2*2*2=3*2^3. In each check we only tested whether 2 divided the number, however if 2 did not divide the number, then we would check 3, 5, 7 etc. until a prime was found which divides the number. This process will work for any whole number greater than 1.

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