Question

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

CAT 2021

Correct option is

**Explanatory Answer :**

We know that the prime factorisation of 28 is 2^2*7^1. That is 28=2*14=4*7.

Also, of course, anything multiplied by 1 is itself the number. (We have also 2*2*7 but [2,2,7] is not a list of distinct digits. )

So the only lists of distinct digits we can use are [4,7] and [1,4,7].

There are 2! permutations of [4,7]and 3! permutations of [1,4,7].

Thus we have counted 8 possibilities. (3*2 + 2)

hence , C is the correct option