Which number among 24963, 24973, 24983 and 24993 is divisible by 7?
24983
Finding the Number Divisible by 7
The question asks us to identify which number among 24963, 24973, 24983, and 24993 is divisible by 7. A number is divisible by 7 if, when divided by 7, the remainder is 0.
To find the answer, we need to perform division for each of the given options by 7 and check the remainder.
Checking 24963 for Divisibility by 7
We divide 24963 by 7:
\( 24963 \div 7 \)
Performing the division:
\( 24963 = 7 \times 3566 + 1 \)
The remainder when 24963 is divided by 7 is 1. Since the remainder is not 0, 24963 is not divisible by 7.
Checking 24973 for Divisibility by 7
We divide 24973 by 7:
\( 24973 \div 7 \)
Performing the division:
\( 24973 = 7 \times 3567 + 4 \)
The remainder when 24973 is divided by 7 is 4. Since the remainder is not 0, 24973 is not divisible by 7.
Checking 24983 for Divisibility by 7
We divide 24983 by 7:
\( 24983 \div 7 \)
Performing the division:
\( 24983 = 7 \times 3569 + 0 \)
The remainder when 24983 is divided by 7 is 0. Since the remainder is 0, 24983 is divisible by 7.
Checking 24993 for Divisibility by 7
We divide 24993 by 7:
\( 24993 \div 7 \)
Performing the division:
\( 24993 = 7 \times 3570 + 3 \)
The remainder when 24993 is divided by 7 is 3. Since the remainder is not 0, 24993 is not divisible by 7.
Conclusion: Identifying Divisibility by 7
Based on the divisions performed, only the number 24983 results in a remainder of 0 when divided by 7. This means that 24983 is exactly divisible by 7.
Revision Table: Checking Number Divisibility by 7
| Number | Division by 7 Result | Remainder | Divisible by 7? |
|---|---|---|---|
| 24963 | \( 3566 \) | 1 | No |
| 24973 | \( 3567 \) | 4 | No |
| 24983 | \( 3569 \) | 0 | Yes |
| 24993 | \( 3570 \) | 3 | No |
Additional Information on Divisibility
Divisibility is a key concept in number theory. It tells us if one number can be divided by another number without leaving a remainder. We explored checking divisibility by 7 through direct division. While there isn't one simple, universally easy rule for divisibility by 7 for all numbers, direct calculation is always a reliable method.
For other numbers, simpler rules exist:
- Divisibility by 2: A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8).
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
- Divisibility by 10: A number is divisible by 10 if its last digit is 0.
Understanding divisibility rules helps in simplifying calculations and solving problems related to factors and multiples.
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