Divisibility Rule of 187

The divisibility rule for 187 is a method by which we can find out if a number is divisible by 187 or not without using the division method. Check whether 561 is divisible by 187 with the divisibility rule.  

Step 1: Check if the number is divisible by 11 and 17, as these are the prime factors of 187. 

Step 2: To check divisibility by 11, sum the digits in odd positions and even positions separately, then find the difference. If the difference is a multiple of 11 (including zero), it’s divisible by 11. For 561, (5+1) - 6 = 0, which is divisible by 11.

Step 3: To check divisibility by 17, subtract 5 times the last digit from the rest of the number. For 561, 56 - (5×1) = 51. Since 51 is not divisible by 17, 561 is not divisible by 187.
 

Learn divisibility rules to help master division. Let’s learn a few tips and tricks for the divisibility rule of 187.

• Know the multiples of 11 and 17: Memorize the multiples of 11 (11, 22, 33,...) and 17 (17, 34, 51,...) to quickly check divisibility. If the number passes both checks, it’s divisible by 187.

• Use negative numbers: If the result from subtraction is negative, consider the absolute value for checking divisibility.

• Repeat the process for large numbers: Keep repeating the divisibility process for large numbers until you reach a small number that is divisible by 11 and 17. For example, check if 3183 is divisible by 187 using the divisibility test. 

For 11: (3+8) - (1+3) = 7, which is not divisible by 11.
For 17: 318 - (5×3) = 303. Repeat: 30 - (5×3) = 15, which is not divisible by 17.

• Use the division method to verify: Use the division method to verify and crosscheck results, helping ensure accuracy and understanding.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.

• Prime factor: A prime number that divides another number exactly, without leaving a remainder.

• Multiple: A product of a number and an integer. For example, multiples of 187 are 187, 374, 561, etc.

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

• Absolute value: The non-negative value of a number without regard to its sign.