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Find the greatest possible length of planks, if three pieces of timber 42m, 49m and 63m long have to be divided into planks of equal lengths.a.7mb.6mc.3.5md.3

Question

Find the greatest possible length of planks, if three pieces of timber 42m, 49m and 63m long have to be divided into planks of equal lengths.a.7mb.6mc.3.5md.3

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the three lengths of timber. The GCD is the largest number that divides all of them without leaving a remainder.

Here are the steps:

  1. List the prime factors of each number:

    • 42 = 2 * 3 * 7
    • 49 = 7 * 7
    • 63 = 3 * 3 * 7

  2. Identify the common prime factors: 7 is the only prime number that is a factor of all three numbers.

  3. Multiply the common prime factors together: 7

So, the greatest possible length of the planks is 7m. Therefore, the answer is a. 7m.

This problem has been solved

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