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What is the number of factors of  243 - 163 - 83 ?

This question was previously asked in
UPSC CDS-I 2025 (Elementary Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 33
  2. 30
  3. 28
  4. 24

Answer (Detailed Solution Below)

Option 1 : 33
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Detailed Solution

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Given:

Expression: 243 − 163 − 83

Calculations:

⇒ 83(27 − 8 − 1)

⇒ 83 × 18

⇒ 512 × 18 = 9216

Prime factorization of 9216:

9216 = 210 × 32

Number of factors = (10 + 1)(2 + 1) = 11 × 3 = 33

∴ The correct answer is: 33

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