How many ordered pairs of (m, n) integers sat | vedclass

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(A) Given the equation $\frac{m}{12} = \frac{12}{n}$.Multiplying both sides,we get $mn = 144$.The prime factorization of $144$ is $2^4 	imes 3^2$.The

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$30$

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(A) Given the equation $\frac{m}{12} = \frac{12}{n}$.Multiplying both sides,we get $mn = 144$.The prime factorization of $144$ is $2^4 	imes 3^2$.The number of positive divisors of $144$ is $(4+1)(2+1) = 5 	imes 3 = 15$.Since $m$ and $n$ can be integers,they can be both positive or both negative.If $m, n > 0$,there are $15$ possible pairs $(m, n)$.If $m, n Therefore,the total number of ordered pairs $(m, n)$ is $15 + 15 = 30$.

How many ordered pairs of $(m, n)$ integers satisfy $\frac{m}{12} = \frac{12}{n}$?

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