If X= (2 raised to power p )x (3 raised to power q ) x (5 raised to power r ) ; p,q,r are 2^nd ,3^rd,4^th multiples of 2,3,5 respectively, then the number of Factors for X is _______

hi

x = 2^4* 3^9 *5^20

the number of factors are same as the nuber of divisors

(4+1)(9+1)(20+1)   including 1 and the number itself

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Jitender

(askIITians expert)

The number of factors for a number

N= a^p * b^q * c^r....

where a, b, c are prime numbers is

(p+1)(q+1)(r+1)....

Here a=2,b=3,c=5

p=4,q=9,r=20

Number of factors= 5*10*21=1050