GMAT Test Tip - Prime Numbers

Here’s a neat little math tip: when you square root a number, you are essentially cancelling out half of that number’s prime factors.

What do we mean by that? Take a look at the square root of 36. Of course, the answer is 6, but let’s break it down and go behind the scenes.

The prime factors of 36 are 2 x 2 x 3 x 3. So what you really have is:

SEE ILLUSTRATION 1

As we said, when you square root a number, you essentially are cancelling out half of each of the distinct primes. In this case, you cut out one 2 and one 3, leaving behind 2 x 3, or 6.

Now, to be clear, we are talking about half of each of the distinct prime factors. Take a look at the square root of 144. The prime factors of 144 are 2 x 2 x 2 x 2 x 3 x 3. There are four 2’s and two 3’s, so cancel out two 2’s and one 3. You are left with 2 x 2 x 3, or 12.

Now you can square root numbers with ease. What’s the square root of 441? Just break it into primes: 3 x 3 x 7 x 7. Cut out a 3 and a 7, you’re left with 21. What is the square root of 784? Primes are 2 x 2 x 2 x 2 x 7 x7, so the answer is 2 x 2 x 7, or 28.

In general, prime numbers are a great tool to utilize when dealing with number properties questions on the GMAT. Stay tuned…we’ll cover other ways in future posts.