Question

1) decomponha os números abaixo em fatores primos
A)16. B)64. C)81. D)12. E)100 F)124. G)8. L)240. I) 180 J)360​

Answer 1

a)

$\begin{matrix}\left\begin{array}{c}16&8&4&2&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\quad\;\;&2\qquad\qquad\quad\;\;&2\qquad\qquad\quad\;\;&2\qquad\qquad\quad\;\;&1\qquad\qquad\quad\;\;\end{array}\right\\\overline{16=2\cdot2\cdot2\cdot2=2^4}\end{matrix}$

b)

$\begin{matrix}\left\begin{array}{c}64&32&16&8&4&2&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad\quad\quad&2\qquad\qquad\qquad\quad\quad&2\qquad\qquad\qquad\quad\quad&2\qquad\qquad\qquad\quad\quad&2\qquad\qquad\qquad\quad\quad&2\qquad\qquad\qquad\quad\quad&1\qquad\qquad\qquad\quad\quad\end{array}\right\\\overline{64=2\cdot2\cdot2\cdot2\cdot2\cdot2=2^6}\end{matrix}$

c)

$\begin{matrix}\left\begin{array}{c}81&27&9&3&1\end{array}\right| \left\begin{array}{c}3\qquad\qquad\quad\;\;&3\qquad\qquad\quad\;\;&3\qquad\qquad\quad\;\;&3\qquad\qquad\quad\;\;&1\qquad\qquad\quad\;\;\end{array}\right\\\overline{81=3\cdot3\cdot3\cdot3=3^4}\end{matrix}$

d)

$\begin{matrix}\left\begin{array}{c}12&6&3&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\quad\;\;&2\qquad\qquad\quad\;\;&3\qquad\qquad\quad\;\;&1\qquad\qquad\quad\;\;\end{array}\right\\\overline{12=2\cdot2\cdot3=2^2\cdot 3}\end{matrix}$

e)

$\begin{matrix}\left\begin{array}{c}100&50&25&5&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad\;\;&5\qquad\qquad\qquad\;\;&5\qquad\qquad\qquad\;\;&5\qquad\qquad\qquad\;\;&1\qquad\qquad\qquad\;\;\end{array}\right\\\overline{100=2\cdot5\cdot5\cdot5=2\cdot5^3}\end{matrix}$

f)

$\begin{matrix}\left\begin{array}{c}124&62&31&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad&2\qquad\qquad\qquad&31\qquad\qquad\qquad&1\qquad\qquad\qquad\end{array}\right\\\overline{124=2\cdot2\cdot31=2^2\cdot 31}\end{matrix}$

g)

$\begin{matrix}\left\begin{array}{c}8&4&2&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\;\;&2\qquad\qquad\;\;&2\qquad\qquad\;\;&1\qquad\qquad\;\;\end{array}\right\\\overline{8=2\cdot2\cdot2=2^3}\end{matrix}$

h)

$\begin{matrix}\left\begin{array}{c}240&120&60&30&15&3&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad\qquad\quad\;\;&2\qquad\qquad\qquad\qquad\quad\;\;&2\qquad\qquad\qquad\qquad\quad\;\;&2\qquad\qquad\qquad\qquad\quad\;\;&3\qquad\qquad\qquad\qquad\quad\;\;&3\qquad\qquad\qquad\qquad\quad\;\;&1\qquad\qquad\qquad\qquad\quad\;\;\end{array}\right\\\overline{240=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^4\cdot 3^2}\end{matrix}$

i)

$\begin{matrix}\left\begin{array}{c}180&90&45&15&5&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad\qquad\quad\;\;&2\qquad\qquad\qquad\qquad\quad\;\;&3\qquad\qquad\qquad\qquad\quad\;\;&3\qquad\qquad\qquad\qquad\quad\;\;&5\qquad\qquad\qquad\qquad\quad\;\;&1\qquad\qquad\qquad\qquad\quad\;\;\end{array}\right\\\overline{180=2\cdot2\cdot3\cdot3\cdot5=2^2\cdot 3^2\cdot5}\end{matrix}$

j)

$\begin{matrix}\left\begin{array}{c}360&180&90&45&15&5&1\end{array}\right| \left\begin{array}{c}2\qquad\qquad\qquad\qquad\qquad\;\;&2\qquad\qquad\qquad\qquad\qquad\;\;&2\qquad\qquad\qquad\qquad\qquad\;\;&3\qquad\qquad\qquad\qquad\qquad\;\;&3\qquad\qquad\qquad\qquad\qquad\;\;&5\qquad\qquad\qquad\qquad\qquad\;\;&1\qquad\qquad\qquad\qquad\qquad\;\;\end{array}\right\\\overline{180=2\cdot2\cdot2\cdot3\cdot3\cdot5=2^3\cdot 3^2\cdot5}\end{matrix}$

Espero ter ajudado!