1970 AHSME Problems/Problem 23
Problem
The number ( is written in base ), when written in the base system, ends with exactly zeros. The value of is
Solution
A number in base that ends in exactly zeros will be divisible by , but not by . Thus, we want to find the highest for which .
There are factors of : , and an extra factor from .
There are factors of : , an extra factor from , and a third extra factor from .
So, will divide . Thus, the answer is .
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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