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Any numbers ending in one are divisible by one. 11, 21, 31, 41, 51, 61 (6)
Any numbers ending in 2 are even and therefore divisible by 2. 12, 22, 32, 42, 52, 62(6)
Numbers ending in 3 only have 2 solutions, which is 33, 63 (1)
Numbers ending in 4 have 2 solutions, since only multiples of 20 from 24 will work. 24, 44 (2)
Any numbers ending in 5 are divisible by five. 15, 25, 35, 45, 55 (5)
Numbers ending in 6 only have 1 solution, which is 36 (1)
Numbers ending with 7 have no solution.
Numbers ending in 8 have 1 solution, which is 48 (1)
Numbers ending in 9 have no solution
All numbers ending in zero can't be divided.
There are a total of 9+6+6+1+2+5+1+1 = 31 numbers that can be divisible by its unit digit.
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21, 22, 24, 25, 31, 32, 33, 35, 36, 41, 42, 45, 48, 51, 52, 55, 61, 62, 63
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