The Singing Hedgehog Guide to:
Prime Factors 8 - Squares

Any square number must have a pair of equal factors, that value being the square root of the number.
This means that we can always group the prime factors of a square number into two equal sets:

Example:
36 = [2 x 3] x [2 x 3], where 2 x 3 = 6 =
√36

We can always multiply or divide by one or more primes to turn a number into a square.

Example: What is the smallest integer that 600 can be multiplied by to make a square number?

We know from before that:
600 = 2 x 2 x 2 x 3 x 5 x 5
We can regroup this:
[2 x 2 x 3 x 5] x [2 x 5]
 
You can see that the right hand set needs another 2 and 3 so we must multiply by 6 to make:
[2 x 2 x 3 x 5] x [2 x 2 x 3 x 5].

Now you need to practise:

downloadable worksheet
(save this file then run it) 

Prime Factors

return to SHG main page