228 LearnersLast updated on May 26th, 2025
Divisibility Rule of 17
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 17.
What is the 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.
Tips and Tricks for Divisibility Rule of 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.
Common Mistakes and How to Avoid Them in Divisibility Rule of 17
The divisibility rule of 17 helps us quickly check if the given number is divisible by 17, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: multiplying the last digit by 5 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 17.
Divisibility Rule of 17 Examples
Problem 1
Is 306 divisible by 17?
Yes, 306 is divisible by 17.
Explanation
To check if 306 is divisible by 17, follow these steps:
1) Multiply the last digit of the number by 5, 6 × 5 = 30.
2) Subtract the result from the remaining digits excluding the last digit, 30 from 30 = 0.
3) The result is 0, therefore 306 is divisible by 17.
Problem 2
Check the divisibility rule of 17 for 493.
Yes, 493 is divisible by 17.
Explanation
To check the divisibility rule of 17 for 493:
1) Multiply the last digit of the number by 5, 3 × 5 = 15.
2) Subtract the result from the remaining digits, excluding the last digit, 49 – 15 = 34.
3) Check if 34 is a multiple of 17, yes, 34 is a multiple of 17 (17 × 2 = 34).
Problem 3
Is -289 divisible by 17?
Yes, -289 is divisible by 17.
Explanation
To check if -289 is divisible by 17, ignore the negative sign and follow the steps:
1) Multiply the last digit of the number by 5, 9 × 5 = 45.
2) Subtract the result from the remaining digits excluding the last digit, 28 – 45 = -17.
3) The result is a multiple of 17, therefore -289 is divisible by 17.
Problem 4
Can 250 be divisible by 17 following the divisibility rule?
No, 250 is not divisible by 17.
Explanation
To check if 250 is divisible by 17, follow these steps:
1) Multiply the last digit of the number by 5, 0 × 5 = 0.
2) Subtract the result from the remaining digits excluding the last digit, 25 – 0 = 25.
3) Check if the result is a multiple of 17. No, 25 is not a multiple of 17.
Problem 5
Check the divisibility rule of 17 for 799.
Yes, 799 is divisible by 17.
Explanation
To check the divisibility rule of 17 for 799, follow these steps:
1) Multiply the last digit of the number by 5, 9 × 5 = 45.
2) Subtract the result from the remaining digits, excluding the last digit, 79 – 45 = 34.
3) Check if the result is a multiple of 17. Yes, 34 is a multiple of 17 (17 × 2 = 34).
FAQs on Divisibility Rule of 17
1.What is the divisibility rule for 17?
2.How many numbers are there between 1 and 100 that are divisible by 17?
3.Is 51 divisible by 17?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 17 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 17?
7.What are some fun ways kids in United States can practice Divisibility Rule of 17 with numbers?
8.What role do numbers and Divisibility Rule of 17 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 17 skills?
Important Glossaries for Divisibility Rule of 17
- 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.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
