Which number among 11368, 11638, 11863 and 12638 is divisible by 11?
11638
Finding a Number Divisible by 11
To determine which number among 11368, 11638, 11863, and 12638 is divisible by 11, we can use the divisibility rule for 11. This rule is a quick way to check divisibility without performing long division.
The Divisibility Rule for 11
A number is divisible by 11 if the difference between the sum of its digits at odd places (from the right) and the sum of its digits at even places (from the right) is either 0 or a multiple of 11 (such as 11, 22, -11, etc.).
Let's apply this rule to each of the given numbers:
Checking Divisibility for Each Number
Number 1: 11368
- Digits from right at odd places (1st, 3rd, 5th): 8, 3, 1
- Sum of digits at odd places: $\small 8 + 3 + 1 = 12$
- Digits from right at even places (2nd, 4th): 6, 1
- Sum of digits at even places: $\small 6 + 1 = 7$
- Difference: $\small 12 - 7 = 5$
Since the difference, 5, is not 0 or a multiple of 11, the number 11368 is not divisible by 11.
Number 2: 11638
- Digits from right at odd places (1st, 3rd, 5th): 8, 6, 1
- Sum of digits at odd places: $\small 8 + 6 + 1 = 15$
- Digits from right at even places (2nd, 4th): 3, 1
- Sum of digits at even places: $\small 3 + 1 = 4$
- Difference: $\small 15 - 4 = 11$
Since the difference, 11, is a multiple of 11, the number 11638 is divisible by 11.
Number 3: 11863
- Digits from right at odd places (1st, 3rd, 5th): 3, 8, 1
- Sum of digits at odd places: $\small 3 + 8 + 1 = 12$
- Digits from right at even places (2nd, 4th): 6, 1
- Sum of digits at even places: $\small 6 + 1 = 7$
- Difference: $\small 12 - 7 = 5$
Since the difference, 5, is not 0 or a multiple of 11, the number 11863 is not divisible by 11.
Number 4: 12638
- Digits from right at odd places (1st, 3rd, 5th): 8, 6, 2
- Sum of digits at odd places: $\small 8 + 6 + 2 = 16$
- Digits from right at even places (2nd, 4th): 3, 1
- Sum of digits at even places: $\small 3 + 1 = 4$
- Difference: $\small 16 - 4 = 12$
Since the difference, 12, is not 0 or a multiple of 11, the number 12638 is not divisible by 11.
Based on the application of the divisibility rule for 11, only the number 11638 resulted in a difference that is a multiple of 11 (which is 11 itself).
Therefore, the number divisible by 11 among the given options is 11638.
Revision Table: Divisibility by 11 Checks
| Number | Sum of Odd Place Digits (from right) | Sum of Even Place Digits (from right) | Difference | Divisible by 11? |
|---|---|---|---|---|
| 11368 | $\small 8+3+1 = 12$ | $\small 6+1 = 7$ | $\small 12-7 = 5$ | No |
| 11638 | $\small 8+6+1 = 15$ | $\small 3+1 = 4$ | $\small 15-4 = 11$ | Yes |
| 11863 | $\small 3+8+1 = 12$ | $\small 6+1 = 7$ | $\small 12-7 = 5$ | No |
| 12638 | $\small 8+6+2 = 16$ | $\small 3+1 = 4$ | $\small 16-4 = 12$ | No |
Additional Information on Divisibility Rules
Divisibility rules are shortcuts for determining if a number is evenly divisible by another number without performing the division. Knowing these rules can save time in calculations and help understand number properties.
- Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
- Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility by 10: A number is divisible by 10 if its last digit is 0.
The divisibility rule for 11, as demonstrated above, is particularly useful for larger numbers.
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