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ਕਦਮ ਦਰ ਕਦਮ

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.

ਜਵਾਬ ਦਿਓ

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