Question

Two wires of length 252cm and 616 cm are to be cut into pieces without wasting any wire. Whats the greatest possible length of pieces

Answer 1

Answer:Two wires with lengths of 448 cm and 616 cm are to be cut into pieces all the same length without remainder. find the greatest possible length of pieces. The greatest possible length is 56 cm in 8 pieces in terms of 448 cm.

Answer 2

Answer:

The greatest possible length of pieces that can be cut from 252cm and 616cm wires without wasting any wire is 28cm.

Step-by-step explanation:

The answer is the GCD of the lengths of two wires 252cm and 616cm.

Using the concept of Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) to solve the problem.

What is GCD/GCF?

GCD/GCF is the greatest number that can divide a set of numbers evenly while leaving the remainder as zero.

In order to determine the GCD of a set of numbers, several methods are available, such as:

1. Prime factorisation method
2. Factoring method
3. Euclid's Algorithm

Here, we will solve using the Prime factorisation method.

What is Prime Factorisation method?

It is a method to determine the prime numbers those when multiplied together forms the original number.

Steps for Prime Factorisation method:

1. In this method, the given number or set of numbers is divided by the smallest prime number, if the remainder is not zero then continue with the next smallest prime number.
2. The resulting quotient(s) is divided by the same or the next smallest prime number and so on until the remainder goes to zero and the original number(s) is completely factorised.
3. Then the common prime factors from the set of numbers are selected and multiplied.
4. The resulting number is the GCD of the set of numbers.

Calculation:

Prime factorisation of 252:

$252 = 2*126\\ =2*2*63\\ =2*2*3*21\\ =2*2*3*3*7$

Prime factorisation of 616:

$616 = 2*308\\ = 2*2*154\\ =2*2*2*77\\ =2*2*2*7*11$

From the prime factors of 252, 616, the common factors are 2,2,7.

Hence, the GCF of 252,616 is 2*2*7 = 28

Hence, the greatest possible length of pieces that the wires can be cut without wasting any wire is 28cm.

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