Divisibility Rule of 17

The divisibility rule for 17 is a method by which we can find out if a number is divisible by 17 or not without using the division method. Check whether 289 is divisible by 17 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 5, here in 289, 9 is the last digit, multiply it by 5. 9 × 5 = 45.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 28 - 45 = -17.

Step 3: As it is shown that -17 is a multiple of 17, therefore, the number is divisible by 17. If the result from step 2 isn't a multiple of 17, then the number isn't divisible by 17.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 17.

• Know the multiples of 17: Memorize the multiples of 17 (17, 34, 51, 68, 85…etc.) to quickly check divisibility. If the result from subtraction is a multiple of 17, then the number is divisible by 17.

• Use the negative numbers: 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 17. 
  For example: Check if 2040 is divisible by 17 using the divisibility test. Multiply the last digit by 5, i.e., 0 × 5 = 0. Subtract the result from the remaining digits, 204 - 0 = 204. Repeat the process for 204. Multiply the last digit by 5, 4 × 5 = 20. Now subtract 20 from the remaining numbers, 20 - 20 = 0. As 0 is considered divisible by 17, 2040 is divisible by 17.

• 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. For example, a number is divisible by 2 if the number ends with even numbers.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 17 are 17, 34, 51, 68, etc.

• Integers: Integers are numbers that include all 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.

• Absolute value: The absolute value of a number is its distance from zero on the number line, without considering direction. It is always a non-negative number.