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There are two long ropes of 18 meters and 24 meters respectively. They should be cut into small sections of the same length. What is the maximum length of each section? How many segments can be cut?
18 = 2 × 3 × 3, 24 = 2 × 2 × 2 × 3, the greatest common factor of 18 and 24 is 2 × 3 = 6, that is, the maximum length of each rope is 6 meters, 18 △ 6 + 24 △ 6 = 3 + 4, = 7 (segments). A: the maximum length of each rope is 6 meters, which can be cut into 7 segments
There are three ropes. The first one is 12 meters long, the second one is 18 meters long, and the third one is 24 meters long. Now we need to cut them into small sections of the same length. How many meters is the maximum length of each section?
12 = 2 × 2 × 3, 18 = 2 × 3 × 3, 24 = 2 × 2 × 2 × 3, the greatest common factor of 12, 18 and 24 is 2 × 3 = 6, that is, the maximum length of each segment is 6m
There are three pieces of iron wire, which are 24, 40 and 56 decimeters long respectively. They should be cut into small pieces of the same length, and no surplus is allowed. How long is the maximum length of each piece? How many pieces can they be cut into?
Factorization
The divisible numbers of 24 are 12, 8, 6, 4, 3 and 2
The divisible numbers of 40 are 20, 10, 8, 5, 4 and 2
The divisible numbers of 56 are 28, 14, 8, 7, 4 and 2
The largest common factor is 8, so each segment is up to 8 meters long,
It can be cut into 24 / 8 + 40 / 8 + 56 / 8 = 3 + 5 + 7 = 15 sections
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