Q109 / 180 · COMEDK 2020 · Mathematics

The remainder obtained when $5^{124}$ is divided by 124 is

  • A
    0
  • Correct answer
    B
    5
  • C
    1
  • D
    2

Solution

We have; $$ \begin{aligned} 5^{124} &=\left(5^{3}\right)^{41} \cdot 5 \\ \text { Now, } 5^{3} &=1 \cdot(\bmod 124) \\ \left(5^{3}\right)^{41} &=1\langle\bmod 124) \\ \left(5^{3}\right)^{41} \cdot 5 &=1 \times 5(\bmod 124)=5(\bmod 124) \end{aligned} $$ So, the remainder obtained when $5^{124}$ is divided by 124 is 5 .

Hence, the correct answer is option: 'B'.

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