Divisibility Rule of 691

The divisibility rule for 691 is a method by which we can find out if a number is divisible by 691 or not without using the division method. Check whether 1382 is divisible by 691 with the divisibility rule.
 

Step 1: Divide the number into two parts: the part before the last three digits and the last three digits. For 1382, the two parts are 1 and 382.

Step 2: Multiply the first part by 691 and compare it with the second part. Calculate 1 × 691 = 691.

Step 3: Subtract the result from Step 2 from the second part: 382 - 691.

Step 4: If the result is zero or a multiple of 691, the number is divisible by 691. In this example, 382 - 691 is not zero or a multiple of 691, so 1382 is not divisible by 691.
 

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 691.
 

• Know the multiples of 691: Memorize the multiples of 691 (691, 1382, 2073, ... etc.) to quickly check divisibility. If the subtraction result is a multiple of 691, the number is divisible by 691.
   
• Use negative numbers: If the result after subtraction is negative, consider it as positive for checking divisibility.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that can be easily checked against 691.
   
• 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: The set of rules used to determine if one number is divisible by another without performing division.
   
• Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 691 are 691, 1382, 2073, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: The process of finding the difference between two numbers by reducing one from the other.
   
• Verification: The process of ensuring the correctness of a result, often by using another method, such as actual division.