# 1 trillion as two factors

1. Dec 31, 2009

### Cesius

Can anyone tell me how to factor 1 trillion in 2 numbers, and none of them have zeroes in them?

Thanks.

2. Dec 31, 2009

### Cesius

The two numbers I got were 262,144 x 3,814,697.266 and 5^12 x 2^12. I'm not sure which one is right because the first one I'm not sure if it's exact and the second one technically has zeroes.

3. Dec 31, 2009

### rphenry

Usually in riddles of this nature the "two numbers" are assumed to be integers.

Perhaps the riddle meant the British definition of "trillion", 10^18, in which case your factors would be 2^18 and 5^18, (262144 and 3814697265625).

4. Dec 31, 2009

### Cesius

I'm American, and it's an American school so I'm pretty sure it mean 10^12.

Thanks though.

5. Dec 31, 2009

### hamster143

It's straightforward to prove that 5^12 x 2^12 is the only factorization into two factors such that neither of the two ends with zero. (Because any factor that has a 2 and a 5 would be divisible by ten.)

6. Dec 31, 2009

### Cesius

It's not that it can't end in zero, it just can't have any zeros in it.

7. Dec 31, 2009

### hamster143

Then some trick must be involved. Either you're allowed to use non-integer factors, or you're allowed to use non-decimal systems.

8. Jan 1, 2010

### HallsofIvy

Staff Emeritus
$2^12= 4096$ and $5^12= 244140625$, both of which have 0s so $(2^12)(5^12($ and with any other two factors at least one would have to have factors of "2" and "5" and so be a multiple of 10.

9. Jan 1, 2010

### Staff: Mentor

1*1717914916

Edit: on the second reading I see hamster already hinted at this solution.

10. Jan 1, 2010

### sjb-2812

Isn't this sum wrong anyway, as 1 trillion (either long or short scale), 10 and 16 are all co-prime to 2, so it cannot end in an odd "digit"? ;)

11. Jan 1, 2010

### Staff: Mentor

No idea what have happened, obviously some finger slip on my side. 1*34771513724319 looks much better.

12. Jan 1, 2010

### Staff: Mentor

262,144 x 3814697.265625 works if one is allowed decimals.

13. Jan 1, 2010

### Cesius

We are allowed decimals. Thanks for the answers Astronuc! And thanks for the help everyone!

14. Jan 2, 2010

### HallsofIvy

Staff Emeritus
It would have helped if you had told us that to begin with! You said "factor one trillion" and that usually means into integer factors.

15. Jan 2, 2010

### FeDeX_LaTeX

Try this: Factor 611939 into two different integer factors. ;)

^^

16. Jan 2, 2010

### Staff: Mentor

You're welcome. I was wondering if one had to have integers which would be impossible given the constraints. I just start dividing 512 by 2 until I found a number without zeros.

On the other hand, one can also divide 212 by 5's, in which case only one division is needed 212/5 = 819.2 and 48828125 = 511.