Question

Write the natural numbers from $102$ to $113$.What fraction of them are prime numbers?

Answer 1

Natural numbers from $102$ to $113$

$=102,103,104,105,106,107,108,109,110,111,112,113$

Numbers divisible by $2$

Number ending with $2,4,6,8,0$ are divisible by $2$

So,$102,104,106,108,110,112$ are not prime.

Numbers divisible by $3$

If sum of digits is divisible by $3,$ it is divisible by $3$

So,$105,111$ are not prime.

Rest all numbers are not divisible by $5,7,11$

$\therefore 103,107,109,113$ are prime

$\therefore$ total numbers$=12$

Number of prime numbers$=4$

$\therefore$ Fraction$=\frac{4}{12}=\frac{1}{3}$