Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

3 x 2^c x d

Hey...

Just wondering if there is a quick and easy way of doing this question?

The number 1104 can be written as 3 x 2^c x d, where c is a whole number and d is a prime number. Work out the value of c and the value of d.

I got the right answer... but i got there by dividing 1104 by 3, writing out the first 15 prime numbers and the first few powers of 2, and seeing which 2 of these numbers would give me 368. Is there a quicker or better way of doing it? (non calculator paper)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 3 x 2^c x d

I'd start the same way you did, dividing by 3, so that would get 2^c x d = 368.
From there, I think the best way is to keep dividing 368 by 2 until you get to an odd number.

368 --> 184 --> 92 --> 46 --> 23

We've divided by 2 four times and got left with 23, which means that 368 = 2^4 x 23.
Therefore 1104 = 3 x 2^4 x 23.

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It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: 3 x 2^c x d

Great thats a much cleaner way. Thanks!

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: 3 x 2^c x d

Basically what you are asking is if a number has any other prime divisors other than 2's and a single 3.  Division is pretty much the only route to go to find this out.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."