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Is the following statement true or false?Explain. There are integers $x,y,$ and $z$ such that $14$ divides $2^x × 3^y × 5^z$.

My guess is false but I don't know how to explain it?Does it have anything to do with the fundamental theorem of arithmetic?

LM2357
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Lim Sook Yee
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1 Answers1

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Here's an intuitive explanation

Yes $14$ does not divide $2^x × 3^y × 5^z$ for any integers $x,y,z$ because

$14=2 × 7$

Since there are no seven's in the expression..It will never fully divide it

LM2357
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