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:
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:
(save this file then run it)
return to SHG main page