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Question
Three pieces of timber 42m, 49m and 63m 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?
Solution
The lengths of three pieces of timber are 42m, 49m and 63m respectively.
We have to divide the timber into equal length of planks.
∴ Greatest possible length of each plank = HCF (42, 49, 63)
Prime factorization:
42 = 2 × 3 × 7
49 = 7 × 7
63 = 3 × 3 × 7
∴ HCF = Product of the smallest power of each common prime factor involved in the numbers = 7
Therefore, the greatest possible length of each plank is 7m.
We now divide the length of each piece by the HCF to determine the total number of planks formed by each piece. i.e. by 7.
We know that;
7 × 6 = 42
7 × 7 = 49
7 × 9 = 63
Therefore, total number of planks formed = 6 + 7 + 9 = 22
Hence, total 22 planks will be formed.
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