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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 _______



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







Grade:10

2 Answers

jitender lakhanpal
62 Points
7 years ago

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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Amit Jain
askIITians Faculty 32 Points
7 years ago

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

 

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