The problem you're dealing with involves finding the greatest common divisor (GCD) of two lengths of wire, 26 metres of brown wire and 20 metres of red wire, so that both wires can be cut into smaller pieces of equal length with no leftover material.

To solve this, we need to determine the largest number that divides both 26 and 20 evenly. This is essentially the GCD (Greatest Common Divisor) of 26 and 20.

Steps to find the GCD of 26 and 20:

1. Start by finding the divisors of both numbers:

   • Divisors of 26: 1, 2, 13, 26
   • Divisors of 20: 1, 2, 4, 5, 10, 20

2. The common divisors are: 1, 2.

3. The greatest of these common divisors is 2.

Answer:

The longest piece Sandy can make is 2 metres.

Would you like a more detailed explanation on finding the GCD or have any further questions?

Here are 5 questions that build on this concept:

1. How can the GCD be found using the Euclidean algorithm?
2. Can Sandy use a different method to divide the wire equally?
3. If the wires were 30 metres and 45 metres, what would the longest equal piece be?
4. How does finding the GCD apply to other real-world scenarios like tiling floors?
5. Could prime factorization help in finding the GCD of two numbers?

Tip: The Euclidean algorithm is a fast way to find the GCD by repeatedly applying the division algorithm.