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.
