P1. (3+7 points) What is the smallest positive integer with precisely 5 positive divisors? What is the smallest positive integer with precisely 60 positive divisors? Show your work and reasoning.

smallest positive integer with 5 positive divisor is 16

smallest positive integer with 60 positive divisor is 5040

Step-by-step explanation:

given data

precisely positive divisors = 5

precisely positive divisors = 60

solution

we take here is express as

= (x+1) × (y+1) × (z+1)

so put here now x is 4

and z = y = 0 and a is least integer more than 1 it will be 2

and b and c ≥ 1

and is = 1

so is

is =  = 16  

so smallest positive integer with 5 positive divisor is 16

and

same like 60 positive divisors

dn = ( a1+1 ) × ( a2+1 ) × ( a3+1 )  ............ ( an+1 )

n =

n = 7 × 5 × 3² ×

n = 5040

smallest positive integer with 60 positive divisor is 5040

answer: do you still need this?

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this