Question
A rectangular courtyard is $20m$ $16\ cm$ long and $15m$ $60\ cm$ broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.
✓
Answer
Length of the rectangular courtyard $= 20m$
$16\ cm = 2,016\ cm$
Breadth of the rectangular courtyard $= 15m$
$60\ cm = 1,560\ cm$
Least possible side of the square stones used to pave the rectangular courtyard
$= HCF$ of $(2,016$ and $1,560)$
Prime factorization of $2,016 =2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7$
Prime factorization of $1,560 = 2 \times 2 \times 2 \times 3 \times 5 \times 13$
$HCF$ of $(2,016, 1,560) = 2 \times 2 \times 2 \times 3= 24$
Least possible side of square stones used to pave the rectangular courtyard is $24 \ cm.$
Number of square stones used to pave the rectangular courtyard
= Area of rectangular courtyard Area of square stone $= 2016\ cm \times 1560\ cm (24\ cm) 2 = 5460$
Thus, the least number of square stones used to pave the rectangular courtyard is $5,460.$
$16\ cm = 2,016\ cm$
Breadth of the rectangular courtyard $= 15m$
$60\ cm = 1,560\ cm$
Least possible side of the square stones used to pave the rectangular courtyard
$= HCF$ of $(2,016$ and $1,560)$
Prime factorization of $2,016 =2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7$
Prime factorization of $1,560 = 2 \times 2 \times 2 \times 3 \times 5 \times 13$
$HCF$ of $(2,016, 1,560) = 2 \times 2 \times 2 \times 3= 24$
Least possible side of square stones used to pave the rectangular courtyard is $24 \ cm.$
Number of square stones used to pave the rectangular courtyard
= Area of rectangular courtyard Area of square stone $= 2016\ cm \times 1560\ cm (24\ cm) 2 = 5460$
Thus, the least number of square stones used to pave the rectangular courtyard is $5,460.$
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