Answer :
Lixin has three ribbons of lengths 160 cm, 192 cm, and 240 cm, respectively. She wishes to cut all the ribbons into equal pieces without any leftover ribbon. Find the largest possible length of each piece of ribbon.
Let the largest possible length of each piece of ribbon be x cm. Then, the number of equal pieces in each ribbon would be:Length of the first ribbon = 160 cm Number of equal pieces = 160/x Length of the second ribbon = 192 cm Number of equal pieces = 192/x Length of the third ribbon = 240 cm Number of equal pieces = 240/x Since the number of pieces has to be a whole number, we can say that:x must be a factor of 160, 192, and 240.The common factors of 160, 192, and 240 are 1, 2, 4, 8, 16. Therefore, the largest possible length of each piece of ribbon is given by the highest common factor (HCF) of 160, 192, and 240.So, HCF(160, 192, 240) = 16 Therefore, the largest possible length of each piece of ribbon is 16 cm.
After factoring each ribbon length (160, 192, and 240 cm), we get a total of 5 common factors; 1, 2, 4, 8, and 16. The highest of these factors, which are factors of all three ribbon lengths, is 16cm. Therefore, the largest possible length of each piece of ribbon is 16cm.
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