three pieces of timber of 42,49 and 63 m long have to be divided into planks of the same length . what is the greatest possible length of each plank?
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Step-by-step explanation:
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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