Which two whole numbers, neither containing any zeros, when multiplied together equal exactly 1,000,000,000?
A: 512 and 1953125
The factorization of this number is 10^9
which can be broken down into its prime factors of (2 x 5)^9
so 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
If we mix any 2 with any 5 we will get 10 and the number will end in a zero due to multiplication by 10
Therefore we must keep the 2s and the 5s separate from one another
2^9 is 512 and 5^9 is 1953125
These two factors (each with no zeros) will multiply out to 1 billion!
