Answer :
Final answer:
The greatest possible length for each piece of ribbon when cutting ribbons of 336 cm and 504 cm into pieces of equal length is 168 cm, as it is the greatest common divisor of both lengths.
Explanation:
To find the greatest possible length of each piece when cutting two ribbons of lengths 336 cm and 504 cm into pieces of equal length, we need to find the greatest common divisor (GCD) of these two lengths. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
Here are the steps to find the GCD of 336 and 504:
- List the factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 112, 168, 336.
- List the factors of 504: 1, 2, 3, 4, 6, 7, 8, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.
- Identify the highest factor that appears on both lists: The largest number that appears on both lists is 168.
- Therefore, the greatest possible length for each piece is 168 cm.
Thus, the ribbon can be cut into pieces where each piece is 168 cm in length.