Answer:
No, Sara can only cut 8 equal-sized pieces with maximum longitude and no wood left over.
Step-by-step explanation:
For finding which longitude meets the requirements (to be the longest with no wood left over) we must decompose 18 and 30 in their prime factors.
For doing so, we look for the prime numbers that divide 18 and 30, as follows
18 | 2 30 | 2
9 | 3 15 | 3
3 | 3 5 | 5
1 1
Thus 18=2*3*3, and 30=2*3*5.
The maximun number that divides both 18 and 30 must be 2*3=6, because these are the prime numbers that both decompositions have in common.
6 represents the maximum longitude for a piece of wood with no leftovers.
Since 18/6=3, and 30/6=5, we can only obtain 5+3=8 wood pieces from the boards.
Of course, we can cut in a half the 8 pieces obtaining 16 equal-sized pieces of wood, but unfortunately, they won't be the longest pieces possible.
