Find the remainder when 67107 is divided by 7.
A. 4
B. 2
C. 1
D. 6
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \frac{{{{67}^{107}}}}{7} \cr & Or,\,\frac{{{{\left( {7 \times 9 + 4} \right)}^{107}}}}{7} \cr & {\text{The}}\,{\text{remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}} \cr & \frac{{{4^{107}}}}{7} \cr & Or,\,\frac{{{4^3}}}{7} \cr & Or,\,\frac{{64}}{7} \cr & {\text{Required}}\,{\text{Remainder}} = 1 \cr} $$Join The Discussion
Comments ( 6 )
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Wrong ans ???
Right is 2 ??
Wrong ans ???
Right is 2 ??
why are u giving the wrong ans
the ans is remainder=2
67^107/7
Or, (7*9+4)107/7
And the remainder 107/6 = 5
The remainder will be same as
4^5 / 7
Or, 16 * 64 /7
Or, 2 * 1 /7
Required Remainder = 2.
ans= 2
how that step came after 4^107/7 to 4^3/7