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

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph