- #1
doggydan42
- 170
- 18
Homework Statement
Five consecutive multiples of 8 have a 9-digit product of ##49xyz2160##. What is the value of ##x\cdot y \cdot z##?
Homework Equations
I am unsure of what equations would be relevant.
The Attempt at a Solution
I tried breaking the number into its parts: ##4\cdot 10^8+9\cdot 10^7+x\cdot 10^6+y\cdot 10^5+...+6\cdot 10##; though, I wasn't sure what I could do next.
I also realized that the 9-digit number must be divisible by ##8\cdot \frac{n!}{(n-5)!}## for some natural number n.
How would I go about solving this with mathematical rigor, and what would be the fastest way to solve it?
Thank you in advance.
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