Question

If m, p, and t are distinct positive prime numbers, then m3pt has how many different positive divisors greater than 1 ?'

Answer 1

Answer:

15

Step-by-step explanation:

Each positive divisor of N = m³pt has a prime factorization made up from:

• 1, m, m² or m³  ( 4 possibilities )
• 1 or p ( 2 possibilities )
• 1 or t ( 2 possibilities )

So in total there are 4 × 2 × 2 = 16 positive divisors.  However, one of these is 1, corresponding to choosing "1" in each of the three steps above.  So excluding this we get...

The number of different positive divisors of N greater than 1 is 15.