Question

if the prime factorization of natural number N is 2 ^ 3 into 3 ^ 2 into 5 to the power 2 into 7 write the number of consecutive zeros in n

Answer 1

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{expression}\mathrm{is}{2}^3\times 3^2\times 5^2\times 7\mathrm{which}\mathrm{can}\mathrm{be}\mathrm{re}-\mathrm{written}\mathrm{as}{2}^2\times 5^2\times 3^2\times 7 \\ \mathrm{We}\mathrm{know}\mathrm{that}2\times 5=10,\mathrm{so}\mathrm{ones}2\mathrm{and}\mathrm{ones}5\mathrm{will}\mathrm{form}\mathrm{single}0\mathrm{at}\mathrm{unit}\text{'}\mathrm{s}\mathrm{digit}. \\ \mathrm{Then},2^2\times 5^2=100\mathrm{which}\mathrm{forms}2\mathrm{zeroes}. \\ \mathrm{Therefore},\mathrm{consecutive}\mathrm{number}\mathrm{of}\mathrm{zeroes}=2 \end{gathered}$$
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