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+1
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avatar+545 

Emma plays with her square unit tiles by arranging all of them into different shaped rectangular figures. (For example, a 5 by 7 rectangle would use 35 tiles and would be considered the same rectangle as a 7 by 5 rectangle). Emma can form exactly ten different such rectangular figures that each use all of her tiles. What is the least number of tiles Emma could have?

 Jul 3, 2019
 #1
avatar+6046 
+1

since they have to be different

1x1 = 1

1x2 = 2

1x3 = 3

1x4=4

2x2 = 4

1x5=5

1x6=6

2x3=6

1x7=7

1x8=8

 

46 tiles

 Jul 3, 2019
 #2
avatar
0

I think you misunderstood the question

Guest Jul 3, 2019
 #4
avatar+106539 
+2

We are looking for the first positive integer with exactly 20  divisors

 

I believe this is

 

2^4 * 3 * 5 =  240

 

The divisors  are

1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240

 

She can form rectangles

1 x 240              6 x 40

2 x 120              8  x 30

3 x  80              10 x 24          

4 x  60              12 x 20

5 x  48              15 x 16

 

 

cool cool cool

 Jul 3, 2019

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