Question

Let K= 168 x 900 = 151,200. How many

positive integer divisors doe- Khave? (Ask
about a clever way to calculate the number of
divisors from the prime factorization of a
number.)

Answer 1

To calculate the number of positive integer divisors of a number, find the exponents of the prime factors and add 1 to each exponent. Then multiply all the results together to get the total number of divisors.

Step-by-step explanation:

To calculate the number of positive integer divisors of a number from its prime factorization, you need to find the exponents of the prime factors and add 1 to each exponent. Then multiply all the results together to get the total number of divisors.

In this case, the prime factorization of K is 2^4 * 3^2 * 5^2. So the number of divisors is (4+1) * (2+1) * (2+1) = 5 * 3 * 3 = 45.

Therefore, there are 45 positive integer divisors of K.