Question

a) How many positive integers are divisors of 243,000,000? b) How many positive integers divide both 243,000,000 and 1,440,000

Answer 1

Note That: . where pi's are distinct primes

Then number of positive divisor of n =

a)

Total number of positive divisor = (6+1)(5+1)(6+1)

=7×6×7 =  

b) number of positive divisor of both given number = number of positive divisor of their g.c.d

Now, g.c.d.(243000000,1440000)=

Now,   

Number of positive divisor, = (6+1)(2+1)(4+1)=7×3×5=