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CTET PAPER II 2021 · PYQ · Number Theory / Prime Factorization · hard

The number of distinct prime factors of the largest 6-digit number is

  1. A.3
  2. B.4
  3. C.5
  4. D.6✓ Correct

Explanation

The largest 6-digit number is 999999. Factorize: 999999 = 3³ × 7 × 11 × 13 × 37. Let's verify: 999999 = 999 × 1001 = (3 × 333) × (7 × 143) = (3 × 3 × 111) × (7 × 11 × 13) = 3³ × 37 × 7 × 11 × 13. The distinct prime factors are 3, 7, 11, 13, 37—that's 5 distinct primes. Hmm, only 5. Let me recheck: 999999 = 3 × 333333 = 3 × 3 × 111111 = 9 × 111111 = 9 × 3 × 37037 = 27 × 37037 = 27 × 7 × 5291 = 27 × 7 × 11 × 481 = 27 × 7 × 11 × 13 × 37. So 999999 = 3³ × 7 × 11 × 13 × 37. Distinct primes: {3, 7, 11, 13, 37} = 5 primes. So answer is 5, option (3).
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