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Divisibility rules are shortcut tests to determine if a number is evenly divisible by another without performing long division. They exploit patterns in decimal representation.
الصيغة
n is divisible by d if remainder(n÷d) = 0 | Divisibility rules: even if last digit divisible by 2, by 3 if digit sum divisible by 3
- n
- Number to Check (integer)
- d
- Divisor (integer)
- r
- Remainder (integer)
دليل خطوة بخطوة
- 1÷2: last digit is even
- 2÷3: digit sum divisible by 3
- 3÷4: last two digits divisible by 4
- 4÷5: ends in 0 or 5
- 5÷6: divisible by both 2 and 3
- 6÷9: digit sum divisible by 9
- 7÷10: ends in 0
أمثلة محلولة
الإدخال
1,260
النتيجة
Sum of digits = 9 → divisible by 3, 9. Last digit 0 → by 2, 5, 10. So also by 6.
الإدخال
7,777
النتيجة
Digit sum 28 — not divisible by 3. Ends in 7 — not 2, 5, 10.
أسئلة شائعة
What are divisibility rules?
Divisibility rules are shortcuts to check if a number is divisible by another without performing long division.
What is the divisibility rule for 9?
A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 729: 7+2+9=18, and 18 is divisible by 9.
Is every even number divisible by 4?
No. A number is divisible by 4 only if its last two digits form a number divisible by 4. For example, 24 yes, but 22 no.
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