Divisibility Rule of 330

The divisibility rule for 330 involves checking if a number is divisible by each of the factors of 330 without using the division method. 330 can be broken down into its prime factors: 2, 3, 5, and 11. Therefore, a number is divisible by 330 if it is divisible by each of these factors. Let's check whether 660 is divisible by 330 using this rule.

Step 1: Check divisibility by 2. A number is divisible by 2 if it is even. 660 is even, so it is divisible by 2.

Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 660 is 6 + 6 + 0 = 12, which is divisible by 3.

Step 3: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. 660 ends in 0, so it is divisible by 5.

Step 4: Check divisibility by 11. A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11 (including 0). For 660, (6+0) - 6 = 0, which is a multiple of 11.

Since 660 satisfies all these conditions, it is divisible by 330.

Understanding divisibility rules helps students master division. Here are some tips and tricks for the divisibility rule of 330:

• Memorize the conditions for each factor: Remember the divisibility rules for 2, 3, 5, and 11 to quickly check if a number is divisible by 330.

• Use modular arithmetic: If the result of a condition seems unclear, use simple arithmetic or modular arithmetic to verify divisibility.

• Break it down: For larger numbers, break them into smaller parts and check each part's divisibility by 2, 3, 5, and 11.

• Use the division method to verify: Verify your result by using the division method to ensure accuracy and to gain a better understanding.

• Divisibility rule: A set of rules used to determine if a number is divisible by another without division.

• Prime factors: The prime numbers that multiply together to give the original number. For 330, these are 2, 3, 5, and 11.

• Even number: A number divisible by 2.

• Sum of digits: The total obtained by adding all digits of a number, used to check divisibility by 3.

• Modular arithmetic: A method of arithmetic for integers, where numbers wrap around upon reaching a certain value (the modulus).