+586 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?
+6250 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
+129899 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
