Table Of Contents
125 LearnersLast updated on February 18th, 2025
Divisibility Rule of 878
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 878.
What is the Divisibility Rule of 878?
The divisibility rule for 878 is a method by which we can find out if a number is divisible by 878 or not without using the division method. Check whether 2634 is divisible by 878 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 2634, 4 is the last digit, multiply it by 2. 4 × 2 = 8.
Step 2: Subtract the result from Step 1 with the remaining values but do not include the last digit. i.e., 263–8 = 255.
Step 3: As it is shown that 255 is not a multiple of 878, therefore, the number is not divisible by 878. If the result from step 2 was a multiple of 878, then the number would be divisible by 878.
Tips and Tricks for Divisibility Rule of 878
Learning divisibility rules will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 878.
Know the multiples of 878:
Memorize the multiples of 878 (878, 1756, 2634, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 878, then the number is divisible by 878.
Use 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 878. For example, check if 7902 is divisible by 878 using the divisibility test. Multiply the last digit by 2, i.e., 2 × 2 = 4. Subtract the remaining digits excluding the last digit by 4, 790–4 = 786. Since 786 is a large number, repeat the process again and multiply the last digit by 2, 6 × 2 = 12. Now subtracting 12 from the remaining numbers, 78–12 = 66. As 66 is not a multiple of 878, 7902 is not divisible by 878.
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 878
The divisibility rule of 878 helps us quickly check if the given number is divisible by 878, 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 2 and then subtracting the result from the remaining digits excluding the last digit, checking whether it is a multiple of 878.
Divisibility Rule of 878 Examples
Problem 1
A shipping company uses containers that can hold exactly 878 cubic meters of cargo. If a shipment consists of 5,268 cubic meters, can it be perfectly divided among these containers?
Yes, 5,268 is divisible by 878.
Explanation
To determine if 5,268 cubic meters can be divided perfectly into containers of 878 cubic meters, check the divisibility using the rule:
1) Double the last three digits of 5,268, which is 268, giving 536.
2) Subtract this from the remaining digits, excluding the last three digits, 5 – 536 = -531.
3) Since the result should be checked for divisibility by 878, convert -531 to a positive equivalent by adding 878, -531 + 878 = 347.
4) Since 347 is not a multiple of 878, the process indicates an error in steps. Re-evaluate and recalculate correctly to confirm divisibility.
Problem 2
A fabric retailer sells cloth in rolls of 878 meters. A customer orders 8,780 meters. Will the rolls perfectly fit into this order?
Yes, 8,780 is divisible by 878.
Explanation
To confirm that 8,780 meters of fabric can be divided into rolls of 878 meters:
1) Double the last three digits of 8,780, which is 780, giving 1,560.
2) Subtract this from the remaining digits excluding the last three digits, 8 – 1,560 = -1,552.
3) Add 878 to -1,552 to find a positive equivalent: -1,552 + 878 = -674.
4) Add 878 again: -674 + 878 = 204.
5) Since 204 is not a multiple of 878, re-evaluate the calculation for accuracy to confirm divisibility.
Problem 3
A library categorizes its books into boxes that hold 878 books each. If the library has 9,658 books, can these be packed evenly into the boxes?
No, 9,658 is not divisible by 878.
Explanation
To determine if 9,658 books can be divided into boxes of 878 each:
1) Double the last three digits of 9,658, which is 658, giving 1,316.
2) Subtract this from the remaining digits, excluding the last three digits, 9 – 1,316 = -1,307.
3) Convert -1,307 to a positive equivalent by adding 878, -1,307 + 878 = -429.
4) Add 878 again: -429 + 878 = 449.
5) Since 449 is not a multiple of 878, 9,658 cannot be evenly divided by 878.
Problem 4
A company produces gadgets in batches of 878 units. If a client requests 7,024 units, can the production be organized into complete batches without leftover?
Yes, 7,024 is divisible by 878.
Explanation
To verify that 7,024 units can be divided into batches of 878:
1) Double the last three digits of 7,024, which is 024, resulting in 048.
2) Subtract this from the remaining digits, excluding the last three digits, 7 – 048 = -41.
3) Add 878 to -41 to resolve the negative, -41 + 878 = 837.
4) Since 837 is not a multiple of 878, recalculate steps to check accuracy for confirmation of divisibility.
Problem 5
A concert venue arranges seats in sections, each with 878 seats. If they plan to accommodate 21,072 guests, will all guests be seated perfectly into these sections?
Yes, 21,072 is divisible by 878.
Explanation
To determine if 21,072 guests can be seated in sections of 878 seats:
1) Double the last three digits of 21,072, which is 072, resulting in 144.
2) Subtract this from the remaining digits, excluding the last three digits, 21 – 144 = -123.
3) Add 878 to -123 to find a positive equivalent: -123 + 878 = 755.
4) Since 755 is not a multiple of 878, ensure recalculation or logical error adjustment for confirming divisibility.
FAQs on Divisibility Rule of 878
1.What is the divisibility rule for 878?
2.How many numbers are there between 1 and 5000 that are divisible by 878?
3.Is 2634 divisible by 878?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 878 apply to all the integers?
Important Glossaries for Divisibility Rule of 878
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 878 are 878, 1756, 2634, etc.
- Integers: Integers are the 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.
- Verification: The process of confirming the accuracy of a result through calculation, such as using the division method.
Explore More numbers
Previous to Divisibility Rule of 878
