A rectangular floor is 18m long and 12m broad. If it is to be paved with Square tiles same size, find the greatest size of each tile and also find the number of tiles required.
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It is given that a rectangular hall is 18m 72cm long and 13m 20cm broad which means that rectangular hall is 1872 cm long and 1320 cm broad.
The given integers 1872 and 1320 can be factorised as follows:
1872=2×2×2×2×3×3×13
1320=2×2×2×3×5×11
We know that HCF is the highest common factor, therefore, the HCF of 1872 and 1320 is:
HCF=2×2×2×3=24
Therefore, maximum side of the square is 24 cm and
Since, area of rectangular courtyard is 1872×1320=2471040 and area of the square tile is 24×24=576.
Now, the number of tiles required is:
24×24
1872×1320
=
576
2471040
=4290
Hence, the least possible number of such tiles is 4290.
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