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Class 8-9-10, JEE & NEET
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Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length. What is the greatest possible length of each plank? How many planks are formed?
The lengths of three pieces of timber are 42 m, 49 m and 63 m, respectively.
We have to divide the timber into equal length of planks.
∴ Greatest possible length of each plank = HCF(42, 49, 63)
$42=2 \times 3 \times 7$
$49=7 \times 7$
$63=3 \times 3 \times 7$
∴ HCF = Product of smallest power of each common prime factor in the numbers = 7
Therefore, the greatest possible length of each plank is 7 m.
Now, to find the total number of planks formed by each of the piece, we divide the length of each piece by the HCF, i.e. by 7.
We know that;
$7 \times 6=42$
$7 \times 7=49$
$7 \times 9=63$
Therefore, total number of planks formed $=6+7+9=22$
Hence, total 22 planks will be formed.