If $$63 \times 65 \times 67 \times 69$$ is divided by 12 then the remainder obtained is

Solution: 

Principle used to solve :Rem (A x B) = Rem. (A) x Rem. (B)

A/q

When divided by 12

Rem. (63 x 65 x 67 x 69) = Rem. (63) x Rem.(65) x Rem.(67) x Rem.(69) 

The common multiple of 12 samller than all the above nos. is 60. So taking 60 as reference.     

Rem. (63) x Rem.(65) x Rem.(67) x Rem.(69)  = Rem. (3 x 5 x7 x9) = Rem.(945) 

945 leaves a remainder of 9 when divided by 12, as 936 is the closest multiple of 12 before 945.   

Hence Answer 9