How many positive integers smaller than $1{,}000{,}000$ are powers of $2$, but are not powers of $8$? you may find it useful to consider that $2^{10}=1024$?

Question

Emily Hensley

Mathematics

22 March, 22:10

How many positive integers smaller than $1{,}000{,}000$ are powers of $2$, but are not powers of $8$? you may find it useful to consider that $2^{10}=1024$?

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Answers (1)

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Vincent Freeman · Answer 1

2^19 is the highest you can go lower than 1,000,000.

8^6 is the highest you can go lower than 1,000,000

just Subtract the Exponents.

19-6=13

2^13 so there are 13 integers that are the power of 2 but not the power of 8 and less than 1,000,000.