CAT4MBA

Find the number of rational numbers a/b such that
I. 0 < a/b < 1
II. a and b are co-prime natural numbers and
III. Product of a and b is 15!
a. 2^7
b. 2^6
c. 2^5
d. 2^15

Solution:

The number of prime numbers involved in the factorization of 15! are 6. So the number of ways in which it can be expressed as a product of two co - prime factors is 2^(6 - 1) = 2^5. Hence there are 2^5 ways of finding such a and b such that:
I. 0 < a/b < 1
II. a and b are co-prime natural numbers and
III. Product of a and b is 15!

So, the number of rational numbers a/b are 2^5

Thank You

Ravi Raja

"III. Product of a and b is 15!"
Can u xplain hw a,b satisfies ds condn. Plz provide xample....

Regards,
Dipanjan.....

Good Question

15!=2^11*3^6*5^3*7^2*11*13

32 number possible

Here are the value of A

2^11 for this case value of b=3^6*5^3*7^2*11*13
3^6 for this case value of b=2^11*5^3*7^2*11*13
5^3
7^2
11
13
2^11*5^3
2^11*7^2
2^11*11
2^11*13
3^6*5^3
3^6*7^2
3^6*11
3^6*13
5^3*7^2
5^3*11
5^3*13
7^2*11
7^2*13
11*13
13*11*2^11
13*11*7^2
13*7^2*5^3
13*11*5^3
13*7^2*3^6
13*11*3^6
13*7^2*2^11
13*5^3*3^6
11*7^2*5^3
11*7^2*3^6
11*5^3*3^6
11*13*7^2*5^3

Little Star