How far can you go with the powers?
Number Theory
Level
3
What is the maximum powers of 2 that can divide?
The answer is 4096.
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1 solution
By definition, (a / b)^n = (a^n) / (b^n). Notice the pattern: 10/2 = 5, 100/4 = 25 - this goes to show that the first definition is correct. So using the definition: (10^12) / (2^n) = 5^n. Finding n, it's 12. The max power is 4096.