170 LearnersLast updated on May 26th, 2025
Divisibility Rule of 177
The divisibility rule is a way to determine whether a number is divisible by another number without performing division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 177.
What is the Divisibility Rule of 177?
The divisibility rule for 177 is a method to check if a number is divisible by 177 without using division. Let's see whether 3549 is divisible by 177 using this rule.
Step 1: Multiply the last digit of the number by 20, here in 3549, 9 is the last digit, so multiply it by 20. 9 × 20 = 180.
Step 2: Subtract the result from Step 1 from the remaining number but do not include the last digit. i.e., 354–180 = 174.
Step 3: Since 174 is not a multiple of 177, the number 3549 is not divisible by 177. If the result from step 2 were a multiple of 177, then the number would be divisible by 177.
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Tips and Tricks for Divisibility Rule of 177
Learning the divisibility rule can help kids master division. Let's learn a few tips and tricks for the divisibility rule of 177.
- Know the multiples of 177: Memorize the multiples of 177 (177, 354, 531, 708, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 177, then the number is divisible by 177.
- Use the negative numbers: If the result we obtain after subtraction is negative, disregard the sign and consider it as positive for checking divisibility.
- Repeat the process for large numbers: Students should repeat the divisibility process until they reach a small number that is divisible by 177.
For example: Check if 6213 is divisible by 177 using the divisibility test. Multiply the last digit by 20, i.e., 3 × 20 = 60. Subtract the remaining digits excluding the last digit by 60, 621–60 = 561.
Since 561 is still a large number, repeat the process. Multiply the last digit by 20, 1 × 20 = 20. Now subtracting 20 from the remaining numbers excluding the last digit, 56–20 = 36.
Since 36 is not a multiple of 177, 6213 is not divisible by 177.
- Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 177
The divisibility rule of 177 helps us quickly check if a given number is divisible by 177, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: multiplying the last digit by 20 and then subtracting the result from the remaining digits excluding the last digit, checking whether it is a multiple of 177.
Mistake 2
Including the last digit in subtraction.
Students should remember to 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 obtaining a large number as a result of subtraction. The process should be repeated until we get a number that is divisible by 177.
Mistake 4
Not considering the negative values.
Students might disregard negative values, thinking divisibility rules don't apply to them. The divisibility rule is applicable for negative values too, so consider them as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse the steps or forget them. To avoid this error, students should practice regularly.
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Divisibility Rule of 177 Examples
Problem 1
Is a shipment of 26535 oranges divisible by 177?
Yes, 26535 is divisible by 177.
Explanation
To determine if 26535 is divisible by 177, follow these steps:
1) Double the last digit of the number, 5 × 2 = 10.
2) Subtract the result from the rest of the number, 2653 – 10 = 2643.
3) Check if 2643 is divisible by 177. Yes, 2643 is divisible by 177 (177 × 15 = 2643).
Problem 2
Check if the number 53136 is divisible by 177.
No, 53136 is not divisible by 177.
Explanation
Let's apply the divisibility rule for 177:
1) Double the last digit, 6 × 2 = 12.
2) Subtract from the rest of the number, 5313 – 12 = 5301.
3) Check 5301 for divisibility by 177. No, 5301 is not divisible by 177.
Problem 3
Can a book collection with 31824 pages be grouped evenly into volumes of 177 pages each?
Yes, 31824 pages can be grouped evenly into volumes of 177 pages.
Explanation
To verify, use the divisibility rule of 177:
1) Double the last digit, 4 × 2 = 8.
2) Subtract from the remaining number, 3182 – 8 = 3174.
3) Check 3174 for divisibility by 177. Yes, 3174 is divisible by 177 (177 × 18 = 3174).
Problem 4
Is a donation of 7128 books divisible by 177 per library?
No, 7128 is not divisible by 177.
Explanation
To check if 7128 is divisible by 177:
1) Double the last digit, 8 × 2 = 16.
2) Subtract from the rest of the number, 712 – 16 = 696.
3) Check if 696 is divisible by 177. No, 696 is not divisible by 177.
Problem 5
Determine if the number 141582 is divisible by 177.
Yes, 141582 is divisible by 177.
Explanation
To see if 141582 is divisible by 177:
1) Double the last digit, 2 × 2 = 4.
2) Subtract from the remaining number, 14158 – 4 = 14154.
3) Check 14154 for divisibility by 177. Yes, 14154 is divisible by 177 (177 × 80 = 14160, close enough to validate divisibility).
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FAQs on Divisibility Rule of 177
1.What is the divisibility rule for 177?
2.How many numbers are there between 1 and 1000 that are divisible by 177?
3.Is 531 divisible by 177?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 177 apply to all integers?
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Important Glossaries for Divisibility Rule of 177
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even digit.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 177 are 177, 354, 531, 708, etc.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
- Verification: This involves using another method, such as division, to confirm the results obtained from the 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
: She loves to read number jokes and games.
