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1. 65536

   Factor 65536 by dividing out the smallest prime that goes in, again and again.

2. \vdots

   5 more divisions…

3. 2048 = 2 \times 1024

   2 is the smallest prime dividing 2048.

4. 1024 = 2 \times 512

   2 is the smallest prime dividing 1024.

5. 512 = 2 \times 256

   2 is the smallest prime dividing 512.

6. 256 = 2 \times 128

   2 is the smallest prime dividing 256.

7. 128 = 2 \times 64

   2 is the smallest prime dividing 128.

8. 64 = 2 \times 32

   2 is the smallest prime dividing 64.

9. 32 = 2 \times 16

   2 is the smallest prime dividing 32.

10. 16 = 2 \times 8

    2 is the smallest prime dividing 16.

11. 8 = 2 \times 4

    2 is the smallest prime dividing 8.

12. 4 = 2 \times 2

    2 is the smallest prime dividing 4. That leaves a prime, so we stop.

13. 2 = 2 \times 1

    2 is the smallest prime dividing 2. That leaves a prime, so we stop.

14. 65536 = 2^{16}

    Collect equal primes as powers.

15. d(65536) = (16+1) = 17

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

Atbildēt uz šo jautājumu

65536 = 2^{16}