# 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

$2^12= 4096$ 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

### Astronuc

Staff Emeritus
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

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

### Astronuc

Staff Emeritus
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.