Question

total number of factors of a natural number N is 45. what is the maximum number of prime numbers that can divide N without leaving a remainder. Please do answer this​

Answer 1

Answer:

3

Step-by-step explanation:

Solution: If can factorize the number N into its prime factors as follows N = aw x bx x cy x dz x... where a, b, c, d are prime numbers, Then, number of factors of N = (w + 1 )(x + 1 )(y + 1 )(z + 1)...

Here, the number of factors of N = 45 In order to maximize the number of prime factors of N, we express 45 such that it cannot be factorized any further. 45 = 3 x 3 x 5 N = a2 x b2 x c4 N can have a maximum of 3 prime factors.

Answer is 3