Divisibility Rule of 657

The divisibility rule for 657 helps determine if a number is divisible by 657 without using division. Let's check whether 1971 is divisible by 657 using the divisibility rule.

Example:

Step 1: Find the sum of the digits of the number. For 1971, the sum is 1 + 9 + 7 + 1 = 18.

Step 2: Check if this sum, 18, is divisible by 3 (since 657 is divisible by 3), which it is.

Step 3: Also, check if the number is divisible by 219 (since 657 = 3 × 219). For 1971, perform 1971 ÷ 219 = 9.

Step 4: Since 1971 is divisible by both 3 and 219, it is divisible by 657.

Understanding the divisibility rule will help students master division. Here are some tips and tricks for the divisibility rule of 657.

• Know the factors: Memorize the factors of 657, which are 3 and 219. If a number is divisible by both, it is divisible by 657.
   
• Use the sum of digits: If the sum of the digits of a number is divisible by 3, the number is divisible by 3, a factor of 657.
   
• Repeat the process for large numbers: For larger numbers, continue breaking them down using these factors until you reach a smaller, more manageable number.
   
• Use division for verification: As a cross-check, use traditional division to verify that the number is indeed divisible by 657.

• Divisibility rule: A set of guidelines to determine if one number can be divided by another without a remainder.
   
• Factors: Numbers that multiply together to form another number, such as 3 and 219 for 657.
   
• Sum of digits: The result of adding all the digits in a number, used in checking divisibility by 3.
   
• Verification: The process of using division to confirm if a number is divisible by another.
   
• Integer: A whole number that can be positive, negative, or zero.