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GATE 2024 EC – Question 5

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

The greatest prime factor of $(3^{199}-3^{196})$ is

  1. 13
  2. 17
  3. 3
  4. 11

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Show answer and explanation

Correct answer: (A) 13

Explanation

$3^{199}-3^{196}=3^{196}(3^3-1)=3^{196}\times26=3^{196}\times2\times13$. The prime factors are 2, 3 and 13, so the greatest is 13.