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# 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? - Mathematics

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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?

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#### 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
Hence, the greatest possible length of each plank is 7m.

Concept: Euclid’s Division Lemma
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