Leysa hvaða stærðfræði vandamál
Jafnvægi, afleiður, heildar, fylki, þríhyrningar, frumtölur, tölfræði eða orðavandamálið sem kennarinn brýtur í sundur.
Skref fyrir skref
- 65536
Factor 65536 by dividing out the smallest prime that goes in, again and again.
- \vdots
5 more divisions…
- 2048 = 2 \times 1024
2 is the smallest prime dividing 2048.
- 1024 = 2 \times 512
2 is the smallest prime dividing 1024.
- 512 = 2 \times 256
2 is the smallest prime dividing 512.
- 256 = 2 \times 128
2 is the smallest prime dividing 256.
- 128 = 2 \times 64
2 is the smallest prime dividing 128.
- 64 = 2 \times 32
2 is the smallest prime dividing 64.
- 32 = 2 \times 16
2 is the smallest prime dividing 32.
- 16 = 2 \times 8
2 is the smallest prime dividing 16.
- 8 = 2 \times 4
2 is the smallest prime dividing 8.
- 4 = 2 \times 2
2 is the smallest prime dividing 4. That leaves a prime, so we stop.
- 2 = 2 \times 1
2 is the smallest prime dividing 2. That leaves a prime, so we stop.
- 65536 = 2^{16}
Collect equal primes as powers.
- d(65536) = (16+1) = 17
Bonus: the number of divisors is the product of (exponent + 1) over the prime powers.