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

Answer:

each length should be of 50m.

Step-by-step explanation:

total length 42m+49m+63m

=150m÷3= 50m

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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