Divisibility Rule of 169

The divisibility rule for 169 is a method by which we can find out if a number is divisible by 169 or not without using the division method. Check whether 2873 is divisible by 169 with the divisibility rule.
 

Step 1: Take the last two digits of the number, here in 2873, 73 is the last two digits.
 

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last two digits. i.e., 28 - 73 = -45.
 

Step 3: If the result from Step 2 is a multiple of 169, or if after repeating the process it becomes 0 or a multiple of 169, then the number is divisible by 169. In this case, -45 is not a multiple of 169, so 2873 is not divisible by 169.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 169.
 

• Know the multiples of 169: Memorize the multiples of 169 (169, 338, 507, 676, 845, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 169, then the number is divisible by 169.
   
• Use absolute values: If the result we get after the subtraction is negative, we will consider its absolute value 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 169. For example, check if 3380 is divisible by 169 using the divisibility test. Take the last two digits, 80, and subtract from the remaining number, 33 - 80 = -47. Since -47 is not a multiple of 169, 3380 is not divisible by 169.
   
• Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
   

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 169 are 169, 338, 507, 676, etc.
   
• Integers: Integers include all whole numbers, negative numbers, and zero.
   
• Absolute value: The non-negative value of a number without regard to its sign.
   
• Subtraction: Subtraction is a process of finding the difference between two numbers, by reducing one number from another.