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? How many planks are formed?
∵ length of each plank is the same and we are supposed to find plank of greatest possible length.
Therefore, the greatest possible length of each plank must be the HCF of 42, 49 and 63.
So HCF of 42, 49 and 63 -
Prime factors of numbers are -
42 = 2 × 3 × 7
49 = 7 × 7
63 = 3 × 3 × 7
∴ HCF = 7
Therefore, maximum plank length of each plank = 7m
Total available length of plank = 42 + 49 + 63 = 154m
So number of planks of this maximum possible length = 154/7 = 22.