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Number-Theory · Prime-Factorization

Factorize 9999

9999

Krok za krokom

  1. 9999

    Factor 9999 by dividing out the smallest prime that goes in, again and again.

  2. 9999 = 3 \times 3333

    3 is the smallest prime dividing 9999.

  3. 3333 = 3 \times 1111

    3 is the smallest prime dividing 3333.

  4. 1111 = 11 \times 101

    11 is the smallest prime dividing 1111. That leaves a prime, so we stop.

  5. 101 = 101 \times 1

    101 is the smallest prime dividing 101. That leaves a prime, so we stop.

  6. 9999 = 3^{2} \times 11 \times 101

    Collect equal primes as powers.

  7. d(9999) = (2+1) \cdot (1+1) \cdot (1+1) = 12

    Bonus: the number of divisors is the product of (exponent + 1) over the prime powers.

Odhaliť odpoveď
9999 = 3^{2} \times 11 \times 101