Question

How many numbers exist between 100 and 1000 which are divisible by 8

Answer 1

Hello mate.

Thanks for asking this question.

your answer is =>

by using the following formula , you can easily find total number when you are given such questions.

your formula is =>

$\boxed{t_n = a +\:( n-1 ) \:d}$

where ,

$t_n$ = last number divisible by 8.

n = number of the last number divisible by 8.

a = fist number divisible by 8

d = difference between consecutive numbers divisible by 8 = 8.

so ,

as you know that , the first number that is divisible by 8 from 100 is 104.

=> a = 104.

last number that is divisible by 8 upto 1000 is 992.

$=> t_n$ = 992

so , putting these values in our equation , we get ,

$=>t_n$ = a + ( n-1 ) d

=> 992 = 104 + ( n - 1 ) × 8

=> 992 = 104 - 8 + 8n

=> 992 = 96 + 8n

=> 992 - 96 = 8n

=> 896 = 8n

=> n = $\frac {896}{8}$

=> $\boxed{n\:= \:112}$

so ,

$\underline {there \: are \: totally \: 112\:numbers}$
$\underline{between\:100\:and\:1000\:which\:are\: divisible\:by\:8}$



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