Good stuff, Mike.

Obviously it's critical to not solve this one by determining all 30 factors and then reducing that set to the odd values. (Exercise: if you don't know how to quickly determine that there are 30 factors of 1200, do some drills!)

So, as you say, the key to these is deriving a complete set of prime factors.

Here's my approach:

Get the prime factors of 1200:

1200 = 12*100 = 2*2*3*2*5*2*5 = 2^4 * 3^1 * 5^2

Now, utilize the multiplication rules:

odd*odd = odd
even*odd = even

So, the number of odd factors can be determined by calculating the number of factors when x=0 for 2^x. Why? Because then we are left with only odd*odd.

In this case that means we want the number of factors of 2^0 * 3^1 * 5^2, which is (0+1)(1+1)(2+1) = 1*2*3 = 6.

Answer A

Also, consider this approach:

Given a prime factorization of 2^x * 3^y * 5^z, then the number of odd factors will be:
(total number of factors)/(x+1)

Why is it so? (It's just another format of the first approach)


Try it in this problem:

(4+1)(1+1)(2+1)/(4+1) = 6

Answer A

Hi! I saw this and I wanted to suggest a simpler version!

I'm in a sixth grade pre-algebra class. Recently my teacher showed us a very simple and quick way of doing this type of problem.

Example:

First prime factorize the original number - 1200 = 2*2*2*2*3*5*5 = 2^4*3^1*5^2

Then use the plus 1 method on the odd prime integers - (1+1)(2+1) = 6 odd factors

To find even factors, just find the total number of factors - in this case (4+1)(1+1)(2+1) = 30 total factors - and then subtract the number of odd factors 30 total - 6 odd = 24 even factors.


Hope this helped!
Janelle

SnitchSeeker wrote:Hi! I saw this and I wanted to suggest a simpler version!

I'm in a sixth grade pre-algebra class. Recently my teacher showed us a very simple and quick way of doing this type of problem.

Example:

First prime factorize the original number - 1200 = 2*2*2*2*3*5*5 = 2^4*3^1*5^2

Then use the plus 1 method on the odd prime integers - (1+1)(2+1) = 6 odd factors

To find even factors, just find the total number of factors - in this case (4+1)(1+1)(2+1) = 30 total factors - and then subtract the number of odd factors 30 total - 6 odd = 24 even factors.


Hope this helped!
Janelle

Take the GMAT now! You'll ace it, and you can always use it down the line

(Also, kudos to your teacher. If I had learned this sort of nifty arithmetic at age 12, my whole life would've turned out differently.)