# CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

###### CAT Questions | Number Theory | Product of Digits
CAT Questions

The question is about Product of digits. Given the product of digits of a number, we need to find out the number of possible values satisfying the condition. Dealing with digits and base system of a number is a vital component in CAT Number Theory. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 1: How many numbers with distinct digits are possible product of whose digits is 28?

1. 6
2. 4
3. 8
4. 12

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##### Method of solving this CAT Question from Number Theory - Digits: Product of digits of a number is k, find all possible numbers that could result in this.

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.

The question is "How many numbers with distinct digits are possible product of whose digits is 28?"

##### Hence the answer is "8"

Choice C is the correct answer.

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