Kugadzirisa chero nyaya yematekisi

Step by step

1. 100

   Factor 100 by dividing out the smallest prime that goes in, again and again.

2. 100 = 2 \times 50

   2 is the smallest prime dividing 100.

3. 50 = 2 \times 25

   2 is the smallest prime dividing 50.

4. 25 = 5 \times 5

   5 is the smallest prime dividing 25. That leaves a prime, so we stop.

5. 5 = 5 \times 1

   5 is the smallest prime dividing 5. That leaves a prime, so we stop.

6. 100 = 2^{2} \times 5^{2}

   Collect equal primes as powers.

7. d(100) = (2+1) \cdot (2+1) = 9

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

Kuratidza mhinduro

100 = 2^{2} \times 5^{2}