Question

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?

Answer 1

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)
Prime factorisation:
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
Hence, the greatest possible length of each plank is 7 m.