A seamstress has three colors of ribbon: red (126 cm), blue (196 cm), and green (378 cm). She wants to cut them all to the same length with no ribbon wasted. What is the greatest length, in centimeters, that she can make the ribbons?

The greatest length of ribbon that the seamstress can cut from all three ribbons without any waste is 14 cm, which is determined by finding the greatest common divisor (GCD) for the lengths of the three ribbons (126cm, 196cm, and 378cm).

Explanation:

The problem stated in the question is a typical exercise in the mathematical concept of greatest common divisor (GCD). The greatest common divisor is the largest number that can evenly divide a set of numbers. In this case, we are asked to find the greatest length of ribbon that can be cut from all three ribbons (red, blue, and green) without wasting any part of them.

Start with the lengths of the ribbons: Red = 126 cm, Blue = 196 cm, and Green = 378 cm. What we have to do is find the GCD of 126, 196, and 378.

To solve the problem, you can use either the prime factorization method, the factor listing method, or the division method. If you use the prime factorization method, for instance, you will get the same highest power for the common prime factors and then multiply them to find the GCD. The GCD of 126, 196, and 378 is 14. Thus, the maximum length of ribbon that can be cut from all three ribbon colors without waste is 14 cm.

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