Question

How many three-digit numbers are divisible by its one digits?

Answer 1

ok, just list them out , first of, 111 divided by 1 ,right?

Answer 2

then 222 divided by 2, ok right?

Answer 3

hence we have total 10 numbers.

Answer 4

But the final answer is 420, and I don't get how to get that answer

Answer 5

oh, I misunderstand the question, I am so sorry. It says 3 digit number, no need the same.
that is ì you have 123, then 123 divided by 1, 123 divided by 3 but not 2, then 123 doesn't satisfy the condition.

Answer 6

so, you have to have a very complicated process to get that, not just as I wrote. I am so sorry.

Answer 7

It's ok, but do you know a method to find it out?

Answer 8

I am thinking. for abc if a=b=c, we have 10 numbers as shown

Answer 9

Wonder where is number theory student??

Answer 10

Let start with 1, like 11c, we have 10 more number start with 11 , let check, hopefully we get something
112 check

Answer 11

It looks like you have to calculate each digit separately and add up the 9 digits (0 does not divide).
Say for digit 1, then we have all 3-digit numbers ending in 1, i.e.
101, 111, 121, 131, 141,.....991 for a total of (99-10)+1=90 numbers
We need to add 1 because both 101 and 991 are included.
For digit 2, we do the same,
102,112,122,.....992, so there are also 90 numbers.
For digit 3, we need to work slightly differently. Since 103 and 113 are not divisible by 3, we need to start at 123, we can finish at 993, since 993 is divisible by 3.
123, 153, 183, ....993 for a total of (99-12)/3+1 = 29+1=30 numbers.
For digit 4, we have
104, 124, 144, ....984 .....
Continue this way, you will find 9 numbers that add up to 420 as you said earlier.