Divisibility Rule of 645

The divisibility rule for 645 is a method by which we can determine if a number is divisible by 645 without performing the division operation. Check whether 1290 is divisible by 645 with the divisibility rule.

Step 1: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. Here, 1290 ends with 0, so it is divisible by 5.

Step 2: Check divisibility by 129, as 645 = 5 × 129. Divide the number obtained by removing the last digit by 2 (since 129 is divisible by 3 after checking its sum of digits, 1 + 2 + 9 = 12, which is divisible by 3). So, 129 → 12. Remove the last digit of 1290 to get 129, and divide by 2 → 12 / 2 = 6. Check if the result, 6, is a multiple of 129.

Step 3: As 6 is not divisible by 129, 1290 is not divisible by 645.

Learning divisibility rules will help students master division. Let’s learn a few tips and tricks for the divisibility rule of 645.

• Know the multiples of 645: Memorize the multiples of 645 (645, 1290, 1935, ...etc.) to quickly check divisibility. If the result from subtraction or division is a multiple of 645, then the number is divisible by 645.

• Use negative numbers wisely: If the result obtained after subtraction is negative, consider it as positive for checking divisibility.

• Repeat the process for large numbers: Continue the divisibility process until you reach a small number that is divisible by 645. 
  
  For example: Check if 7745 is divisible by 645 using the divisibility test.
  
  Check divisibility by 5; since 7745 ends with 5, it is divisible by 5.
  
  Remove the last digit to get 774, and check divisibility by 129 using the same steps as above.
  
  Since 774 is not divisible by 129, 7745 is not divisible by 645.

• Use the division method to verify: Use the division method as a way to verify and crosscheck results. This helps in verification and learning.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number without directly dividing.

• Multiples: Results obtained from multiplying a number by an integer. For example, multiples of 645 are 645, 1290, 1935, ...

• Integers: Numbers that include whole numbers, negative numbers, and zero.

• Subtraction: The process of finding the difference between two numbers by reducing one number from another.

• Division: A mathematical operation where a number is evenly distributed into equal parts.