TCS Company Numerical Ability Number System

34. If N is a natural number and Nˆ3 has 16 factors then how many maximum factors can Nˆ4 have?

Read Solution (Total 3)

If N^3 has 16 factors,
then
N^4 will have 25 factors and N is equal to a product of two co-prime numbers.
11 years agoHelpfull: Yes(14) No(1)

Let , N=A*B
Then Nˆ3=Aˆ3 * bˆ3.
No of factors= (3+1)*(3+1)=16.
So, Nˆ4= Aˆ4 * Bˆ4
Hence, no of factors= (4+1) * (4+1) = 25
8 years agoHelpfull: Yes(1) No(0)
solve by using prime factorizatio

consider a term 6

then 6^3=2^3*3^3

then by rule factor (3+1)*(3+1)= 4*4 =16

therefor 6^4 = 2^4*3^4 =(4+1)*(4+1) = 5*5= 25 ans
8 years agoHelpfull: Yes(0) No(0)

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