Question

16. Let N denote the number of all natural numbers n such that n is divisible by a prime
p> √n and p < 20. What is the value of N?​

Answer 1

Answer:

THE ANSWER TO THIS QUESTION IS N=72

Step-by-step explanation:

GIVEN:  p>√n and p∠20

THEORY: If the number is divisible by a prime then the number has to be composite as any prime cannot divide another perfectly itself (this case is ignored).

SOLVING:

Taking cases p can only be positive to ensure that √n is positive

if p=1

then √n<1

n<1

No such n exists.

if p=2

then √n<2

n<4

n=4

if p=3

then √n<3

n<9

n=6,8 (Ignoring repetitions)

if p=4

then √n<4

n<16

n=9,10,12,14,15  

if p=5

then √n<5

n<25

n=16,18,20,21,22,24

if p=6

then √n<6

n<36

n=25,26,27,28,30,32,33,34,35

Continuing the series

N=1+2+5+6+9+.....

we obtain the answer.