1 trillion as two factors

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In summary, the conversation discusses how to factor one trillion into two numbers without any zeroes. The two numbers that were suggested were 262,144 x 3,814,697.266 and 5^12 x 2^12. However, it was later clarified that decimals were allowed, making the solution 262,144 x 3814697.265625. Another method to factor one trillion without any zeroes is to divide 212 by 5's, resulting in 819.2 and 48828125 = 511.2/5.
  • #1
Cesius
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Can anyone tell me how to factor 1 trillion in 2 numbers, and none of them have zeroes in them?

Thanks.
 
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  • #2
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
Cesius said:
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.

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

Thanks though.
 
  • #5
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
It's not that it can't end in zero, it just can't have any zeros in it.
 
  • #7
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
[itex]2^12= 4096[/itex] and [itex]5^12= 244140625[/itex], both of which have 0s so \(\displaystyle (2^12)(5^12(\) 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
1*1717914916

Edit: on the second reading I see hamster already hinted at this solution.
 
  • #10
Borek said:
1*1717914916

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
No idea what have happened, obviously some finger slip on my side. 1*34771513724319 looks much better.
 
  • #12
Cesius said:
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.

262,144 x 3814697.265625 works if one is allowed decimals.
 
  • #13
We are allowed decimals. Thanks for the answers Astronuc! And thanks for the help everyone!
 
  • #14
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
Try this: Factor 611939 into two different integer factors. ;)

^^
 
  • #16
Cesius said:
We are allowed decimals. Thanks for the answers Astronuc! And thanks for the help everyone!
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.
 

What is the definition of "1 trillion as two factors"?

1 trillion as two factors refers to the mathematical representation of 1 trillion as the product of two whole numbers. In other words, it is finding two numbers that when multiplied together, result in 1 trillion.

What are the factors of 1 trillion?

The factors of 1 trillion are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000, 200000, 500000, 1000000, 2000000, 5000000, 10000000, 20000000, 50000000, 100000000, 200000000, 500000000, 1000000000, 2000000000, and 5000000000.

What are the possible combinations of two factors that give 1 trillion?

There are many possible combinations of two factors that give 1 trillion, including: 1 and 1 trillion, 2 and 500 billion, 4 and 250 billion, 5 and 200 billion, 8 and 125 billion, 10 and 100 billion, and so on.

Why is 1 trillion often used as an example for finding two factors?

1 trillion is often used as an example for finding two factors because it is a very large number that can be difficult to comprehend. By breaking it down into two smaller numbers, it becomes easier to understand and work with in mathematical equations.

How can I find the two factors of 1 trillion?

To find the two factors of 1 trillion, you can use various mathematical methods such as trial and error, prime factorization, or the quadratic formula. There are also online calculators and tools available that can quickly calculate the factors for you.

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