Question:medium

In the series given below how many 8s are there each of which is exactly divisible by its preceding as well as succeeding numbers?
2, 8, 3, 8, 2, 4, 8, 2, 4, 8, 6, 8, 2, 8, 2, 4, 8, 3, 8, 2, 8, 6

Show Hint

Since the number is 8, its only single-digit divisors are 1, 2, 4, and 8. Therefore, any 8 surrounded by numbers containing 3, 5, 6, 7, or 9 can be instantly crossed out without performing any division.
Updated On: Jun 11, 2026
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Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Fix the condition.
We count every $8$ that is divisible by both its left neighbour and its right neighbour.
Step 2: Recall what divides 8.
Among small numbers, $8$ is divisible by $1,2,4$ but not by $3$ or $6$.
Step 3: Scan early triplets.
$2,8,3$ fails ($3\nmid 8$); $3,8,2$ fails; the triplet $4,8,2$ works since $4\mid 8$ and $2\mid 8$. That is one.
Step 4: Continue scanning.
$4,8,6$ fails ($6\nmid 8$); $6,8,2$ fails; the triplet $2,8,2$ works. That is two.
Step 5: Finish the scan.
$4,8,3$ fails, $3,8,2$ fails, $2,8,6$ fails, so no further valid $8$ appears.
Step 6: Total the count.
Exactly two $8$s satisfy the rule.
\[ \boxed{2} \]
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