171 LearnersLast updated on May 26th, 2025
Divisibility Rule of 178
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 178.
What is the Divisibility Rule of 178?
The divisibility rule for 178 is a method by which we can find out if a number is divisible by 178 or not without using the division method. Check whether 7128 is divisible by 178 using the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 7128, 8 is the last digit, multiply it by 2. 8 × 2 = 16
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 712–16 = 696.
Step 3: As it is shown that 696 is a multiple of 178, therefore, the number is divisible by 178. If the result from step 2 isn't a multiple of 178, then the number isn't divisible by 178.
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Tips and Tricks for Divisibility Rule of 178
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 178.
- Know the multiples of 178: Memorize the multiples of 178 (178, 356, 534, 712, 890, … etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 178, then the number is divisible by 178.
- 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 178.
For example: Check if 3560 is divisible by 178 using the divisibility test. Multiply the last digit by 2, i.e., 0 × 2 = 0.
Subtract the remaining digits excluding the last digit by 0, 356–0 = 356. As 356 is a multiple of 178, 3560 is divisible by 178.
- Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 178
The divisibility rule of 178 helps us to quickly check if the given number is divisible by 178, 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 that are multiplying the last digit by 2 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 178.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number to result in after subtraction. The process should be repeated until we get the smallest number that is divisible by 178.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to the negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse the steps or forget the steps, to avoid the error students should practice regularly.
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Divisibility Rule of 178 Examples
Problem 1
Is 3562 divisible by 178?
No, 3562 is not divisible by 178.
Explanation
To determine if 3562 is divisible by 178, follow these steps:
1) Double the last digit of the number, 2 × 2 = 4.
2) Subtract the result from the remaining digits excluding the last digit, 356 – 4 = 352.
3) Check if 352 is a multiple of 178. No, 352 is not a multiple of 178.
Problem 2
Check the divisibility rule of 178 for 7124.
Yes, 7124 is divisible by 178.
Explanation
To check if 7124 is divisible by 178, perform the following:
1) Double the last digit of the number, 4 × 2 = 8.
2) Subtract the result from the remaining digits excluding the last digit, 712 – 8 = 704.
3) Check if 704 is a multiple of 178. Yes, 704 is a multiple of 178 (178 × 4 = 704).
Problem 3
Is 5346 divisible by 178?
No, 5346 is not divisible by 178.
Explanation
Follow these steps to check the divisibility of 5346 by 178:
1) Double the last digit of the number, 6 × 2 = 12.
2) Subtract the result from the remaining digits excluding the last digit, 534 – 12 = 522.
3) Check if 522 is a multiple of 178. No, 522 is not a multiple of 178.
Problem 4
Can 1780 be divisible by 178 following the divisibility rule?
Yes, 1780 is divisible by 178.
Explanation
To check if 1780 is divisible by 178, use the following method:
1) Double the last digit of the number, 0 × 2 = 0.
2) Subtract the result from the remaining digits excluding the last digit, 178 – 0 = 178.
3) Check if 178 is a multiple of 178. Yes, 178 is a multiple of 178 (178 × 1 = 178).
Problem 5
Check the divisibility rule of 178 for 890.
No, 890 is not divisible by 178.
Explanation
To determine if 890 is divisible by 178, perform these steps:
1) Double the last digit of the number, 0 × 2 = 0.
2) Subtract the result from the remaining digits excluding the last digit, 89 – 0 = 89.
3) Check if 89 is a multiple of 178. No, 89 is not a multiple of 178
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FAQs on Divisibility Rule of 178
1.What is the divisibility rule for 178?
2.How many numbers are there between 1 and 1000 that are divisible by 178?
3.Is 534 divisible by 178?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 178 apply to all the integers?
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Important Glossaries for Divisibility Rule of 178
- 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 178 are 178, 356, 534, 712, etc.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
- Integer: An integer is a whole number that can be positive, negative, or zero.
- Verification: Verification involves checking the accuracy of results through another method, such as using division to confirm divisibility.
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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.
