Question

If 44= 8 (mod 12),113 =5(mod 12 ) ,then 44×113=______(MOD 12)is

Answer 1

I'll solve it without using formulas. I hope you understand.

44≡8(mod 12) can be expressed as 12p+8=44. (p is quotient here.)

113≡5(mod 12) can be expressed as 12q+5=113. (q is quotient here.)

By multiplying each other, $(12p+8)(12q+5)$ ≡ 44×113(mod 12)

Without really expanding, we can find out all the terms except 40 is a multiple of 12. So all those cancel out.

40≡4(mod 12) and therefore 44×113≡4(mod 12).

Answer 2

Answer :

44 x 113 = 4 (mod 12)