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.
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Important Questions from Divisibility and Remainder
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
