Divisibility Rule of 165

The divisibility rule for 165 is a method by which we can find out if a number is divisible by 165 or not without using the division method. To determine if a number is divisible by 165, it must be divisible by 3, 5, and 11 (since 165 = 3 × 5 × 11).
 

Check whether 2475 is divisible by 165 with the divisibility rule.
 

Step 1: Check divisibility by 3. The sum of the digits of 2475 is 2 + 4 + 7 + 5 = 18, which is divisible by 3.

Step 2: Check divisibility by 5. The last digit of 2475 is 5, which is divisible by 5.

Step 3: Check divisibility by 11. Alternate sum and subtract the digits: (2 - 4 + 7 - 5) = 0, which is divisible by 11.

Since 2475 is divisible by 3, 5, and 11, it is divisible by 165.
 

• Learn the divisibility rules for 3, 5, and 11: This will help in quickly checking the divisibility of a number by 165.
   
• Use the alternate sum method for 11: When checking for divisibility by 11, remember to alternate adding and subtracting the digits.
   
• Repeat the process for large numbers: If the number is large, break it down into smaller sections and check each section for divisibility by 3, 5, and 11.
   
• Verify with the division method: Use the division method to cross-check your results, ensuring accuracy in determining divisibility.
   

• Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
   
• Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 165 include 165, 330, 495, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Alternate sum method: A technique used to check divisibility by 11, involving alternating addition and subtraction of a number's digits.
   
• Divisor: A number by which another number is to be divided. In the case of 165, the divisors are 3, 5, and 11.