Divisibility Rule of 199

The divisibility rule for 199 is a method by which we can find out if a number is divisible by 199 or not without using the division method. Check whether 39801 is divisible by 199 with the divisibility rule.

Step 1: Multiply the last digit of the number by 2; here, in 39801, 1 is the last digit, so multiply it by 2. 1 × 2 = 2.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 3980 - 2 = 3978.

Step 3: Check if 3978 is divisible by 199. If yes, then the number is divisible by 199. If the result from Step 2 isn't divisible by 199, then the number isn't divisible by 199.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 199.

• Know the multiples of 199: Memorize the multiples of 199 (199, 398, 597, 796, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 199, then the number is divisible by 199.
   
• Use the negative numbers: If the result we get after the subtraction is negative, we will consider it as positive for checking the divisibility of a number.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 199. 
  
  Example: Check if 59603 is divisible by 199 using the divisibility test. Multiply the last digit by 2, i.e., 3 × 2 = 6. Subtract the remaining digits excluding the last digit from 6, 5960 - 6 = 5954. Still, 5954 is a large number, so we will repeat the process again and multiply the last digit by 2, 4 × 2 = 8. Now subtracting 8 from the remaining numbers excluding the last digit, 595 - 8 = 587. Repeat again: 7 × 2 = 14, 58 - 14 = 44. As 44 is not a multiple of 199, 59603 is not divisible by 199.
   
• 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 verify and also learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 199 if the rule is satisfied.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 199 are 199, 398, 597, etc.
   
• Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
   
• Verification: Verification is the process of confirming that a calculation or result is correct, often by using another method such as actual division.