Question

If you remove the last digit (one’s place) from a 4-digit whole number, the resulting number is a factor of the 4-digit number. How many such 4-digit numbers are present?

Answer 1

900

Explanation:

We assume that your 4-digit number must be in the range 1000 to 9999. Clearly, any number ending in zero will meet your requirement:

1000/100 = 10

3890/389 = 10

However, the requirement cannot be met when the 1s digit is other than zero.

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For some 3-digit number N and some 1s digit x, the 4-digit number will be

4-digit number: 10N+x

Dividing this by N will give ...

(10N+x)/N = 10 remainder x

N will only be a factor of 10N+x when x=0.

So, there are 900 4-digit numbers that meet your requirement. They range from 1000 to 9990.