EC > GATE 2024 > Linear Algebra
The greatest prime factor of 3199-3196 is
Correct : A
The correct answer is Option A: 13.
Start by taking 3196 common from the expression:
3199 - 3196 = 3196 × (33 - 1) = 3196 × (27 - 1) = 3196 × 26
Now factorize 26:
26 = 2 × 13
So the complete factorization is: 2 × 3196 × 13
The prime factors are 2, 3, and 13. Even though 3 appears with a huge exponent, we compare prime factors by their value, not their power. Among 2, 3, and 13 — the greatest is 13.
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