Divisible by 8 Rule Explained
To determine if a number is divisible by 8, we only need to look at the number formed by its last three digits. If the number formed by the last three digits is divisible by 8, then the entire number is divisible by 8.
Number Analysis for Divisibility by 8
Let's apply this rule to the given numbers:
| Number | Last Three Digits | Check: Is (Last 3 Digits) ÷ 8 divisible? | Result |
|---|---|---|---|
| 6816 | 816 | Is $816 \div 8$ divisible? Calculation: $816 \div 8 = 102$. | Yes |
| 6006 | 006 (or 6) | Is $6 \div 8$ divisible? Calculation: $6 \div 8 = 0.75$. | No |
| 5006 | 006 (or 6) | Is $6 \div 8$ divisible? Calculation: $6 \div 8 = 0.75$. | No |
| 6124 | 124 | Is $124 \div 8$ divisible? Calculation: $124 \div 8 = 15.5$. | No |
Final Check: Identifying the Correct Number
Based on the analysis using the divisibility rule for 8:
- 6816: The last three digits (816) are divisible by 8.
- 6006: The last three digits (6) are not divisible by 8.
- 5006: The last three digits (6) are not divisible by 8.
- 6124: The last three digits (124) are not divisible by 8.
Therefore, the only number among the options that is divisible by 8 is 6816.
Similar Questions
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Important Questions from Divisibility and Remainder
What is the sum of the digits of the least number which when divided by 12, 16 and 20 leaves the same remainder 6 in each case and it is divisible by 9?
As nine-digit number 89563x87y is divisible by 72. What is the value of \(\sqrt{7x-3y}\) ?
The greatest number that on dividing 2675 and 2320 leaves the reminder 5 and 6 ,respectively is :
Find the greatest number that exactly divides 2880, 6525 and 8307.
If a 10 - digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest value of y is :
