6. a) Find a seven-digit number, all digits of which are different and which is divisible by all these digits.

b) Does such an eight-digit number exist?

## 6th grade
86.6. a) 7639128. b) It is clear that the record should not contain zero. Since our number is obviously even, it cannot be divisible by five - otherwise it would end in zero. There are eight digits left, the sum of which is not divisible by three, and the digit 3 must be included in the number's record - a contradiction. Therefore, such a number does not exist.

![](https://cdn.mathpix.com/cropped/2024_05_21_55ce716f238acb5de3adg-249.jpg?height=431&width=489&top_left_y=430&top_left_x=361)

Fig. 61