167 LearnersLast updated on May 26th, 2025
Divisibility Rule of 87
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 87.
What is the Divisibility Rule of 87?
The divisibility rule for 87 is a method by which we can find out if a number is divisible by 87 or not without using the division method. Check whether 1044 is divisible by 87 with the divisibility rule.
Step 1: Multiply the last digit of the number by 5, here in 1044, 4 is the last digit, multiply it by 5. 4 × 5 = 20
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 104–20 = 84.
Step 3: As it is shown that 84 is not a multiple of 87, therefore, the number is not divisible by 87. If the result from Step 2 is a multiple of 87, then the number is divisible by 87.
Tips and Tricks for Divisibility Rule of 87
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 87.
- Know the multiples of 87: Memorize the multiples of 87 (87, 174, 261, 348…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 87, then the number is divisible by 87.
- Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and 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 87.
For example: Check if 3483 is divisible by 87 using the divisibility test. Multiply the last digit by 5, i.e., 3 × 5 = 15. Subtract the remaining digits excluding the last digit by 15, 348–15 = 333. Still, 333 is a large number, hence we will repeat the process again and multiply the last digit by 5, 3 × 5 = 15.
Now subtracting 15 from the remaining numbers excluding the last digit, 33–15 = 18. As 18 is not a multiple of 87, 3483 is not divisible by 87.
- 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 87
The divisibility rule of 87 helps us quickly check if the given number is divisible by 87, 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, which are 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 87.
Divisibility Rule of 87 Examples
Problem 1
Is 5223 divisible by 87?
Yes, 5223 is divisible by 87.
Explanation
To check if 5223 is divisible by 87, we can use the divisibility rule for 87:
1) Add the last digit to twice the rest of the number, 3 + 2 × 522 = 3 + 1044 = 1047.
2) Repeat the process: add the last digit to twice the rest of the number, 7 + 2 × 104 = 7 + 208 = 215.
3) Check if 215 is divisible by 87. No, it's not. However, repeat the process again: 5 + 2 × 21 = 5 + 42 = 47. 47 is not divisible by 87, but since we did not reach divisibility, let's check by division. 5223 ÷ 87 = 60, which is an integer, confirming divisibility.
Problem 2
Check the divisibility rule of 87 for 3489.
No, 3489 is not divisible by 87.
Explanation
To use the divisibility rule for 87:
1) Add the last digit to twice the rest of the number, 9 + 2 × 348 = 9 + 696 = 705.
2) Repeat the process: add the last digit to twice the rest of the number, 5 + 2 × 70 = 5 + 140 = 145.
3) Check if 145 is divisible by 87. No, 145 is not a multiple of 87.
Problem 3
Is -783 divisible by 87?
Yes, -783 is divisible by 87.
Explanation
To check if -783 is divisible by 87, ignore the negative sign and consider 783:
1) Add the last digit to twice the rest of the number, 3 + 2 × 78 = 3 + 156 = 159.
2) Repeat the process: add the last digit to twice the rest of the number, 9 + 2 × 15 = 9 + 30 = 39.
3) Check if 39 is divisible by 87. No, 39 is not. However, checking by division, 783 ÷ 87 = 9, confirming divisibility.
Problem 4
Can 198 be divisible by 87 following the divisibility rule?
No, 198 is not divisible by 87.
Explanation
To check if 198 is divisible by 87 using the divisibility rule:
1) Add the last digit to twice the rest of the number, 8 + 2 × 19 = 8 + 38 = 46.
2) Check if 46 is a multiple of 87. No, 46 is not a multiple of 87.
Problem 5
Check the divisibility rule of 87 for 6969.
Yes, 6969 is divisible by 87.
Explanation
To check the divisibility rule of 87 for 6969:
1) Add the last digit to twice the rest of the number, 9 + 2 × 696 = 9 + 1392 = 1401.
2) Repeat the process: add the last digit to twice the rest of the number, 1 + 2 × 140 = 1 + 280 = 281.
3) Check if 281 is divisible by 87. No, 281 is not. However, checking by division, 6969 ÷ 87 = 80.1, hence, a mistake indicates 6969 is not divisible by 87. Check again or through other means to confirm.
FAQs on Divisibility Rule of 87
1.What is the divisibility rule for 87?
2.How many numbers are there between 1 and 1000 that are divisible by 87?
3.Is 261 divisible by 87?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 87 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 87?
7.What are some fun ways kids in United States can practice Divisibility Rule of 87 with numbers?
8.What role do numbers and Divisibility Rule of 87 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 87 skills?
Important Glossary for Divisibility Rule of 87
- 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 87 are 87, 174, 261, 348, etc.
- Integers: Integers are 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: The process of confirming that a result is correct, such as using division to verify results obtained from a divisibility rule.
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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
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