How to Find What a Number is Divisible By?
To determine if a number is divisible by another number, you can use several methods, including divisibility rules and direct division. Divisibility rules provide shortcuts for specific numbers, while direct division offers a definitive answer.
Divisibility rules offer quick ways to check divisibility without performing long division. Here are some common rules:
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Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). Example: 124 is divisible by 2 because its last digit, 4, is even.
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Divisibility by 3: 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.
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Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Example: 1212 is divisible by 4 because 12 is divisible by 4.
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Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. Example: 205 and 100 are both divisible by 5.
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Divisibility by 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8. Example: 1232 is divisible by 8 because 32 is divisible by 8.
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Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Example: 117 is divisible by 9 because 1 + 1 + 7 = 9, which is divisible by 9.
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Divisibility by 10: A number is divisible by 10 if its last digit is 0. Example: 100, 50, and 10 are all divisible by 10.
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Divisibility by 11: A number is divisible by 11 if the alternating sum of its digits is divisible by 11. (Add the first digit, subtract the second, add the third, and so on). Example: 1364: 1 - 3 + 6 - 4 = 0. Since 0 is divisible by 11, 1364 is divisible by 11.
Using Direct Division
The most reliable method to determine divisibility is direct division. If the division results in a whole number (no remainder), then the number is divisible by the divisor. You can use a calculator or perform long division to check.
Practical Insights
- These divisibility rules are helpful for quick mental checks, especially with smaller numbers.
- For larger numbers or complex divisibility questions, using a calculator or programming tools is more efficient.
