What are the Divisibility Rules for Class 6?
Divisibility rules are shortcuts to determine if a number is evenly divisible by another number without performing long division. For Class 6, the most commonly taught rules focus on smaller numbers.
-
Divisibility by 2: A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). Example: 124 is divisible by 2 because the last digit, 4, is even.
-
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.
-
Divisibility by 4: A number is divisible by 4 if its last two digits are divisible by 4. Example: 1236 is divisible by 4 because 36 is divisible by 4.
-
Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5. Example: 125 and 120 are both divisible by 5.
-
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3. This means the last digit must be even, and the sum of the digits must be divisible by 3. Example: 126 is divisible by 6 because it's divisible by both 2 (last digit is 6) and 3 (1 + 2 + 6 = 9, which is divisible by 3).
-
Divisibility by 8: A number is divisible by 8 if its last three digits are divisible by 8. Example: 1232 is divisible by 8 because 32 is divisible by 8.
-
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Example: 126 is divisible by 9 because 1 + 2 + 6 = 9, which is divisible by 9.
-
Divisibility by 10: A number is divisible by 10 if its last digit is 0. Example: 120 is divisible by 10.
-
Divisibility by 11: A number is divisible by 11 if the alternating sum of its digits is divisible by 11. Start with the last digit and subtract the next digit, add the next, and continue alternating. Example: For 1331: 1 - 3 + 3 - 1 = 0, which is divisible by 11, so 1331 is divisible by 11.
These rules provide efficient ways to check divisibility, particularly useful for larger numbers. Remembering these simple rules can significantly improve calculation speed and understanding in mathematics.
