If (27)^999 is divided by 7, then the remainder is:

Question

If $(27)^{999}$ is divided by 7, then the remainder is:

Accepted Answer

We have,

$${{{{\left( {27} \right)}^{999}}} \over 7}$$

= $${{{{\left( {28 - 1} \right)}^{999}}} \over 7}$$

= $${{28\,\lambda  - 1} \over 7}$$

= $${{28\,\lambda  - 7 + 7 - 1} \over \lambda }$$

= $${{7\left( {4\lambda  - 1} \right) + 6} \over 7}$$

$$\therefore\,\,\,$$ Remainder = 6

Solutions · 1