### Number Theory Questions and Solutions

**Question:**

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

A. 6

B. 4

C. 8

D. 12

**Correct Answer: (C)**

**Explanation:**

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.

**Answer Choice (**

**C**

**)**

**Difficulty Level 2**

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