Divisibility Rule of 33

The divisibility rule for 33 is a method by which we can find out if a number is divisible by 33 or not without using the division method. Check whether 396 is divisible by 33 with the divisibility rule.

Step 1: Check if the number is divisible by both 3 and 11. First, we apply the divisibility rule for 3: Add the digits of the number. For 396, 3 + 9 + 6 = 18. Since 18 is divisible by 3, the number passes the first part of the test.

Step 2: Now, apply the divisibility rule for 11: Find the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. For 396, (3 + 6) - 9 = 0. Since 0 is divisible by 11, the number passes the second part of the test.

Step 3: As 396 passes both tests, it is divisible by 33.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 33.

• Know the multiples of 33: Memorize the multiples of 33 (33, 66, 99, 132, 165, etc.) to quickly check divisibility. If the result from the operations is a multiple of 33, then the number is divisible by 33.
   
• Use the divisibility rules for 3 and 11: Ensure the number is divisible by both 3 and 11 to conclude that it is divisible by 33.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by both 3 and 11. For example, check if 5943 is divisible by 33 using the divisibility test. Apply the rule for 3: 5 + 9 + 4 + 3 = 21, which is divisible by 3. Then, for 11: (5 + 4) - (9 + 3) = -3, which is not divisible by 11. So, 5943 is not divisible by 33.
   
• Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

• Divisibility rule: A set of rules used to determine if a number is divisible by another number without direct division.
   
• Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 33 are 33, 66, 99, 132, etc.
   
• Sum of digits: The result of adding all the digits in a number, used in checking divisibility by 3.
   
• Difference of sums: For divisibility by 11, the difference between the sum of digits in odd and even positions.
   
• Integer: A whole number that can be positive, negative, or zero.