Question

Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5

both.​

Answer 1

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• Numbers :- 102 and 998
• Divisible by :- 2 and 5

${\large{\bf{\underline{\underline{\pink{✯ \: To \: \: find \: ✯}}}}}}$

• Natural number

${\Large{\bf{\red{ ꧁ \: \: { \underline{ \underline{Solution}}} \: \: ꧂}}}}$

As the numbers are divisible by both 2 and 5,so their last digit will always be 0.

Hence, the series are 110,120,130,....,990

This is an A.P( Arithmetic Progression) where

• First term = a=110
• Common difference = d=10
• Nth term = $\sf{a_n=990}$

So, according to the question:-

${\bf{\large{\implies{a _n=a+(n-1)d}}}}$

${ \bf{ \large{ \implies{990=110+(n-1)10}}}}$

${\bf{\large{\implies{990 - 110 = (n - 1)10}}}}$

${\bf{\large{\implies{880 = (n - 1)10}}}}$

$\\ {\bf{\large{\implies{ \frac{880}{10} = n - 1}}}}$

${\bf{\large{\implies{88 = n - 1}}}}$

${\bf{\large{\implies{n-1=88}}}}$

${\bf{\large{\implies{n = 88 + 1}}}}$

$\Large { \underline{ \boxed{ \orange{\bf{\large{\implies{ n=89.}}}}}}}$

Thus, the number of natural numbers between 102 and 998 which are divisible by both 2 and 5 is 89.

Answer 2

The number of natural numbers between 102 and 998 which are divisible by both 2 and 5 is 89.