How many 3 digit numbers are there in which product of their digit is 36. Ex: 236, in this.. product of digit is 36?

Options : A) 32 B) 36 C) 21 D) 15

Answer is : C

Solution :

Given :-
1. Each number is 3 digit number
2. Product Of digits is 36

What To Find:- 
How many such numbers are there.

Procedure :-
1. Factors of 36 are  :
                1 X 36
2 X 18
3 X 12
4 X 9
6 X 6
2. Sub Factors are :

        1 X 36   ---> 1 X (1 X 36)  --> Not 3 digit number
      ---> 1 X (2 X 18)  --> Not 3 digit number
      ---> 1 X (3 X 12)  --> Not 3 digit number
  ---> 1 X (4 X 9)   --> 3 digit number

2 X 18   ---> 2 X (1 X 18)  --> Not 3 digit number
                 ---> 2 X (2 X 9)   --> 3 digit number
      ---> 2 X (3 X 6)   --> 3 digit number

3 X 12   ---> 3 X (1 X 12)  --> Not 3 digit number
                ---> 3 X (2 X 6)   --> 3 digit number
      ---> 3 X (3 X 4)   --> 3 digit number

4 X 9    ---> 4 X 9 X 1     --> 3 digit number
               ---> 4 X (3 X 3)   --> 3 digit number
      ---> (2 X 2) X 9   --> 3 digit number
6 X 6    ---> 6 X (6 X 1)   --> 3 digit number
               ---> 6 X (2 X 3)   --> 3 digit number

4. Total 3 digit numbers we got from above list are :
     
149, 194, 491, 491, 914, 941     ---  6
229, 292, 922,                          ---  3
  236, 263, 632, 623. 326, 362     ---  6
334, 343, 433                           ---  3
661, 616, 166                           ---  3
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Total Numbers are :                  ---  21
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