question_answer

LCM of two numbers is 26XX0 where X is an unknown digit, HCF of the numbers is 24. One of them is 7Y8 where Y is an unknown digit. Number of factors of the other number is

A)  28                              

B)  32           

C)  36                  

D)  40

Correct Answer: B

Solution :

Putting \[Y=6\]in 7 Y 8 it gets divisible by 24 26XXO is divisible by 768 \[\therefore \]\[x=8\] \[L\text{ }cm=26880\] \[\frac{HCF\times LCM}{1st\,No.}=2nd\,No.\] \[\frac{26880\times 768}{24}=840\] \[{{2}^{3}}\times {{5}^{1}}\times {{3}^{1}}\times {{7}^{1}}=4\times 2\times 2\times 2=32\]No. of factor =32