Here's a guide on how to determine if a large number is divisible by another number, using divisibility rules:
It's crucial to understand that divisibility rules provide shortcuts to determine whether a number can be divided by another number evenly, without leaving a remainder. These rules are especially helpful with large numbers.
Divisibility Rules Explained
Here are some common divisibility rules.
Divisibility by 1
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Rule: Any integer is divisible by 1.
- Example: 123 is divisible by 1, and 123 / 1 = 123.
Divisibility by 2
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Rule: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- Example: 346 is divisible by 2 because its last digit is 6.
Divisibility by 3
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Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, and 6 is divisible by 3.
Divisibility by 4
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Rule: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Example: 1236 is divisible by 4 because 36 is divisible by 4.
Divisibility by 5
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Rule: A number is divisible by 5 if its last digit is 0 or 5.
- Example: 450 and 125 are both divisible by 5.
Divisibility by 6
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Rule: A number is divisible by 6 if it is divisible by both 2 and 3. (It must satisfy both rules for 2 and 3)
- Example: 732 is divisible by 6 because it's even (divisible by 2) and the sum of its digits (7 + 3 + 2 = 12) is divisible by 3.
Summary Table of Divisibility Rules
| Divisible by | Rule | Example |
|---|---|---|
| 1 | Any integer is divisible by 1 | 57/1 = 57 |
| 2 | Last digit is even (0, 2, 4, 6, or 8) | 234 (last digit is 4) |
| 3 | The sum of digits is divisible by 3 | 123 (1+2+3 = 6, 6/3 = 2) |
| 4 | The number formed by last two digits is divisible by 4 | 1216 (16/4 = 4) |
| 5 | Last digit is 0 or 5 | 625 (last digit is 5) |
| 6 | Is divisible by both 2 and 3 | 732 (even & 7+3+2=12/3=4) |
Practical Insights
- Multiple Checks: For some numbers, you may need to use multiple divisibility rules.
- Large Numbers: These rules simplify checking large numbers without having to perform long division.
- Mental Math: Divisibility rules help improve mental math skills.
By understanding and applying these divisibility rules, you can quickly determine if a large number is divisible by another number without extensive calculations.
