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\title{Divisibility II }
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\section*{Making use of divisibility rules.}

\question{Figure out whether the following numbers are divisible by 2, 3, 5, 7 or 11. Circle the appropriate divisors. \newline
 \newline
 $85785: \quad \emph {2 \quad 3 \quad 5 \quad 7 \quad 11}$ \newline \newline
 $24794: \quad \emph {2 \quad 3 \quad 5 \quad 7 \quad 11}$ \newline \newline
 $80625: \quad \emph {2 \quad 3 \quad 5 \quad 7 \quad 11}$ \newline \newline
 $57233: \quad \emph {2 \quad 3 \quad 5 \quad 7 \quad 11}$ \newline \newline 
 $69286: \quad \emph {2 \quad 3 \quad 5 \quad 7 \quad 11}$
 } 

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\question{List all the prime numbers less than 150. (A prime number is a positive integer that has only two positive divisors, 1 and itself. Note that one is not a prime number.) } 



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\section*{The Fundamental Theorem of Arithmetic.}

\question{Is $2^9 \times 3$ divisible by 2?} 

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\question{Is $2^9 \times 3$ divisible by 5?}

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\question{Is $2^9 \times 3$ divisible by 8?}

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\question{Is $2^9 \times 3$ divisible by 6?}

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\question{Is $2^9 \times 3$ divisible by 12?}

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\question{Is $2^9 \times 3$ divisible by 24?}


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\question{List all the divisors of $2^2 \times 3 \;  \;  (=12)$?}
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\question{List all the divisors of $2^3 \times 3^2  \;\; (=72)$?}
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\question{List all the divisors of $2^9 \times 3  \;\; (=1536)$?}

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\question{The number $A$ is not divisible by 3. Is it possible that the number $2 \times A$ is divisible by 3?}

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\question{The number $A$ is even. Is it true that the number $3 \times A$ is divisible by 6?}

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\question{The number $5 \times A$ is  divisible by 3. Is it true that the number $A$ is divisible by 3?}
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\question{The number $15 \times A$ is divisible by 6. Is it true that the number $ A$ is divisible by 6?}


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