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Find the product of the given number by suitable rearrangement.$125 \times 40 \times 8 \times 25$

Last updated date: 13th Jul 2024
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Hint: For solving such type of questions, it will be easier if somehow we make a pair whose product will be multiple of $10,100,1000, - - -$ OR we can start with multiplying two terms which gives $0$ which simplifies further calculations.
Given that $125 \times 40 \times 8 \times 25$
$= 125 \times 40 \times 8 \times 25 \\ = \left( {125 \times 8} \right) \times \left( {40 \times 25} \right) \\$
$= \left( {125 \times \left( {4 \times 2} \right)} \right) \times \left( {\left( {10 \times 4} \right) \times 25} \right)\left[ {\because 8 = 4 \times 2\& 40 = 10 \times 4} \right] \\ = \left( {\left( {125 \times 4} \right) \times 2} \right) \times \left( {10 \times \left( {4 \times 25} \right)} \right)\left[ {\because \left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)} \right] \\ = \left( {\left( {500} \right) \times 2} \right) \times \left( {10 \times \left( {100} \right)} \right) \\ = \left( {1000} \right) \times \left( {1000} \right) \\ = 1000000 \\$
Hence, the product of the given number is $1000000$