Question

Find the greatest possible length of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same lengt

Answer 1

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Answer 2

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.

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