# A four-digit number that does not contain zeros is divisible by 63. We crossed out one digit from the number

**A four-digit number that does not contain zeros is divisible by 63. We crossed out one digit from the number, and got a number that is also divisible by 63. And then, after deleting another digit, we got a number that is also divisible by 63. What was the original number?**

1. After deleting two digits, we get a two-digit number that is a multiple of 63. And the only two-digit number that is divisible by 63 is the number 63 itself.

2. The desired number is divisible by 63, therefore, it is also divisible by 9 and 7. Since the number does not contain zeros, and numbers whose sum of digits is a multiple of 9 are divisible by 9, it is clear that two digits 9 have been deleted from the four-digit number.

4. Of the three-digit numbers 963, 693 and 639, the number 693 is divisible by 7.

5. And of the four-digit numbers 9693, 6993 and 6939, the number 6993 is divisible by 7.

Answer: 6993.