FACTORS 2:
a) How many different ways can 50 players in a marching band be arranged in rectangle arrangements. (So they are marching in a rectangle formation)?
b) If marching bands vary from 21 to 49 players, which number of players can be arranged in the greatest number of rectangles?
c) Which number of players can be arranged in the shape of a square?
d) Explain how finding factors can help you answer parts (b) and (c).
50
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2 25
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5 5
30
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5 10
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2 5
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
factors of 50 = 1, 2, 5, 10, 25, 50
figure 1 = 1 x 50
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figure 2 = 2 x 25
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figure 3 = 5 x 10
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b)
21 = 1,3,7,21
22 = 1,2,11,22
23 = 1,23
24 = 1,2,3,4,6,8,12,24
25 = 1,5,25
26 = 1,2,13,26
27 = 1,3,9,27
28 = 1,2,4,7,14,28
29 = 1,29
30 = 1,2,3,5,6,10,15,30
31 = 1,31
32 = 1,2,4,8,16,32
33 = 1,3,11,33
34 = 1,2,17,34
35 = 1,5,7,35
36 = 1,2,3,4,9,12,18,36
37 = 1,37
38 = 1,2,19,38
39 = 1,3,13,39
40 = 1,2,4,5,8,10,20,40
41 = 1,41
42 = 1,2,3,6,7,14,21,42
43 = 1,43
44 = 1,2,4,11,22,44
45 = 1,3,5,9,15,45
46 = 1,2,23,46
47 = 1,47
48 = 1,2,3,4,6,8,12,16,24,48
49 = 1,7,49
48 is the number that the greatest number of rectangles can be made into. It can be arranged into 5 rectangles:
1 x 48
2 x 24
3 x 16
4 x 12
6 x 8
c) 25, 36, 49 can be arranged in the shape of a square.
5x5
6x6
7x7
d) It makes it easier because I wrote down all the factors and then I saw which number had the most. If I hadn't done that I would technically be guessing which number would be right for 4b. But, I didn't really need it for 4c because I could just figure out the squares by square roots.