# CAT Practice : Number System

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Product of digits of a number is k, find all possible numbers that could result in this.

## Product of digits

Q.1: How many numbers with distinct digits are possible product of whose digits is 28?
1. 6
2. 4
3. 8
4. 12

Choice C. 8

## Detailed Solution

Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74.

Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.

We cannot have three digits as (2, 2, 7) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

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