155 LearnersLast updated on May 26th, 2025
Divisibility Rule of 578
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 578.
What is the Divisibility Rule of 578?
The divisibility rule for 578 is a method by which we can determine if a number is divisible by 578 without using the division method. Let's check whether 1156 is divisible by 578 using the divisibility rule.
Step 1: Multiply the last digit of the number by 2. Here in 1156, 6 is the last digit, so multiply it by 2. 6 × 2 = 12.
Step 2: Subtract the result from Step 1 with the remaining values, but do not include the last digit, i.e., 115–12 = 103.
Step 3: As it is shown that 103 is not a multiple of 578, the number 1156 is not divisible by 578. If the result from Step 2 were a multiple of 578, then the number would be divisible by 578.
Tips and Tricks for Divisibility Rule of 578
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 578.
- Know the multiples of 578: Memorize the multiples of 578 (578, 1156, 1734, 2312, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 578, then the number is divisible by 578.
- Use the negative numbers: If the result we get after the subtraction is negative, we will ignore 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 578. Example: Check if 3468 is divisible by 578 using the divisibility test. Multiply the last digit by 2, i.e., 8 × 2 = 16. Subtract the remaining digits excluding the last digit by 16, 346–16 = 330. 330 is not divisible by 578, hence 3468 is not divisible by 578.
- 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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 578
The divisibility rule of 578 helps us to quickly check if a given number is divisible by 578, 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: multiply the last digit by 2, then subtract the result from the remaining digits excluding the last digit, and check whether it is a multiple of 578.
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 they have obtained a large number as the result after subtraction. The process should be repeated until we get the smallest number that is divisible by 578.
Mistake 4
Not considering the negative values.
Students often disregard negative values, thinking divisibility rules don't apply to them. However, the divisibility rule is applicable for negative values too. So students should consider negative values as positive while checking for divisibility.
Mistake 5Students often confuse or forget the steps. To avoid errors, students should practice regularly.
Confusing the steps.
Students often confuse or forget the steps. To avoid errors, students should practice regularly.
Divisibility Rule of 578 Examples
Problem 1
Is 1734 divisible by 578?
Yes, 1734 is divisible by 578.
Explanation
To check 1734 for divisibility by 578, we can follow these steps:
1) Divide 1734 by 578 directly.
2) The division gives a quotient of 3 with no remainder.
3) Therefore, 1734 is divisible by 578.
Problem 2
Check the divisibility rule of 578 for 2890.
No, 2890 is not divisible by 578.
Explanation
To verify the divisibility of 2890 by 578, follow these steps:
1) Divide 2890 by 578.
2) The division results in a quotient of 5 with a remainder.
3) Therefore, 2890 is not divisible by 578.
Problem 3
Is 0 divisible by 578?
Yes, 0 is divisible by 578.
Explanation
Any number, including 0, is divisible by any non-zero number.
1) Divide 0 by 578, which results in 0.
2) The quotient is 0 with no remainder.
3) Therefore, 0 is divisible by 578.
Problem 4
Can 462 be divisible by 578 following the divisibility rule?
No, 462 is not divisible by 578.
Explanation
To check if 462 is divisible by 578:
1) Since 462 is less than 578, it cannot be divided without a remainder.
2) Therefore, 462 is not divisible by 578.
Problem 5
Check the divisibility rule of 578 for -1156.
Yes, -1156 is divisible by 578.
Explanation
To verify divisibility of -1156 by 578:
1) Remove the negative sign and divide 1156 by 578.
2) The division results in a quotient of 2 with no remainder.
3) Therefore, -1156 is divisible by 578.
FAQs on Divisibility Rule of 578
1.What is the divisibility rule for 578?
2.How many numbers are there between 1 and 1000 that are divisible by 578?
3.Is 1156 divisible by 578?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 578 apply to all integers?
6.How can children in Saudi Arabia use numbers in everyday life to understand Divisibility Rule of 578?
7.What are some fun ways kids in Saudi Arabia can practice Divisibility Rule of 578 with numbers?
8.What role do numbers and Divisibility Rule of 578 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Divisibility Rule of 578 skills?
Important Glossaries for Divisibility Rule of 578
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 578 are 578, 1156, 1734, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
- Verification: The process of checking the accuracy of results, such as using division to confirm divisibility.
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