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Practise the method.
Prime factors in packing and synchronising cycles
Prime factors in packing and synchronising cycles
Example 1
There are 26 pencils and 39 erasers. Keep 2 pencils and 9 erasers aside. Use everything else to make the greatest possible number of identical packs, with equal numbers of each item in every pack. How many packs?
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Answer: 6
After the reserves, there are 24 pencils and 30 erasers.
Their HCF is 6
6 identical packs use all the items.
Example 2
Two lights first flash together 7 minutes after a show begins. One then flashes every 5 minutes and the other every 6 minutes. The show ends 121 minutes after it begins. At what time, in minutes after the start, do they last flash together before it ends?
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Answer: 97
They coincide every LCM(5,6)=30 minutes.
Start at 7;
the last time below 121 is 97.
Example 3
There are 107 pencils and 115 erasers. Keep 9 pencils and 3 erasers aside. Use everything else to make the greatest possible number of identical packs, with equal numbers of each item in every pack. How many packs?
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Answer: 14
After the reserves, there are 98 pencils and 112 erasers.
Their HCF is 14
14 identical packs use all the items.
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