How many 3-digit numbers are completely divis | vedclass

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Question

(B) The smallest $3$-digit number completely divisible by $6$ is $102$ (since $102 / 6 = 17$).The largest $3$-digit number completely divisible by $6$

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(B) The smallest $3$-digit number completely divisible by $6$ is $102$ (since $102 / 6 = 17$).The largest $3$-digit number completely divisible by $6$ is $996$ (since $996 / 6 = 166$).These numbers form an arithmetic progression where the first term $a = 102$,the common difference $d = 6$,and the last term $a_n = 996$.Using the formula for the $n^{th}$ term of an arithmetic progression: $a_n = a + (n - 1)d$.Substituting the values: $996 = 102 + (n - 1)6$.Subtract $102$ from both sides: $894 = (n - 1)6$.Divide by $6$: $n - 1 = 149$.Therefore,$n = 150$.

How many $3$-digit numbers are completely divisible by $6$?

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