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Number Theory Level 2

How many zeroes are there in $8589934592\times116415321826934814453125$ ?

Note: Do not use a calculator.

1 solution

Chew-Seong Cheong
Oct 19, 2019

$\begin{aligned} P & = 8589934592 \times 116415321826934814453125 \\ & = 2^{33} \times 5^{33} \\ & = 10^{33} \end{aligned}$

Therefore the number of zeros is $\boxed{33}$ .

@Fahim Muhtamlm , $\red{\text{I don't see how you can solve it without a calculator.}}$

I got a bit lucky, I prime factored 8589934592 as 2^33 (and guessed 33)

Elijah L - 1 year, 7 months ago

But you still need a calculator to be sure. I also guessed it.

Chew-Seong Cheong - 1 year, 7 months ago

By prime factoring both of the numbers, you can multiply them.

Fahim Muhtamim - 1 year, 7 months ago

Well yes but I couldn't prime factor 116415321826934814453125

Elijah L - 1 year, 7 months ago