Question

In how many ways can 27300 be written as a product of two numbers

Answer 1

INFINITE

Step-by-step explanation:

We can get product 27300 in infinite ways as it doesn't certain.

Answer 2

Given: 27300

To find: In how many ways can 27300 be written as a product of two numbers

Solution:

N =27300

Number of factors of N = (m + n) (n + 1)

where N=

   a,b = factors of N

   m,n = power of a and b respectively.

Therefore, 27300 = 2 x 2 x 5 x 5 x 3 x 7 x 13

                             =$2^{2} X 3^{1} X 5^{2} X 7^{1} X 13^{2}$

Number of factors of 27300

   = (2 + 1) (1+1) (2 + 1) (1+1) (2 + 1)

   = 3 x 2 x 3 x 2 x 3

   = 108

as N is non-perfect square number

Therefore, Number of ways of expressing the numbers as product of 2 factors or 2 numbers is total factor/2

Hence, 108 /2 = 54

Therefore, there are 54 ways 27300 can be written as a product of two numbers.