Answer:
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 [tex]a^{x} *b^{y} *c^{z}[/tex] 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 [tex]x^{0}[/tex] is = 1
so [tex]a^{x} *b^{y} *c^{z}[/tex] is
[tex]a^{4}[/tex] is = [tex]2^{4}[/tex] = 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 = [tex]p1^{a1} * p2^{a2} * p3^{a3} * ............ pn^{an} *[/tex]
n = 7 × 5 × 3² × [tex]2^{4}[/tex]
n = 5040
smallest positive integer with 60 positive divisor is 5040
