Applying the Divisibility Rule for 4

Oct 13, 2025 by vinooalluri.com 56 views

Introduction

In mathematics, divisibility rules are essential tools that help us determine whether a number is divisible by another number without performing the actual division. These rules are based on the properties of numbers and can be used to simplify complex calculations. In this article, we will focus on the divisibility rule for 4 and apply it to a set of numbers to determine which one is divisible by 4 with no remainder.

What is Divisibility by 4?

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This means that we need to consider the last two digits of the number and check if they form a number that is divisible by 4.

Applying the Divisibility Rule for 4

Let's apply the divisibility rule for 4 to the given numbers:

A. 214133

To check if 214133 is divisible by 4, we need to consider the last two digits, which are 33. The number 33 is not divisible by 4, so 214133 is not divisible by 4.

B. 510056

For 510056, the last two digits are 56. The number 56 is divisible by 4, so 510056 is divisible by 4.

C. 322569

The last two digits of 322569 are 69. The number 69 is not divisible by 4, so 322569 is not divisible by 4.

D. 952217

The last two digits of 952217 are 17. The number 17 is not divisible by 4, so 952217 is not divisible by 4.

E. 214395

The last two digits of 214395 are 95. The number 95 is not divisible by 4, so 214395 is not divisible by 4.

Conclusion

Based on the divisibility rule for 4, we can conclude that the number 510056 is the only one that is divisible by 4 with no remainder.

Why is the Divisibility Rule for 4 Important?

The divisibility rule for 4 is an essential tool in mathematics that helps us determine whether a number is divisible by 4 without performing the actual division. This rule is based on the properties of numbers and can be used to simplify complex calculations. By applying this rule, we can quickly determine whether a number is divisible by 4 and perform calculations more efficiently.

Real-World Applications of the Divisibility Rule for 4

The divisibility rule for 4 has several real-world applications in various fields, including:

Accounting: When performing calculations involving large numbers, the divisibility rule for 4 can help accountants quickly determine whether a number is divisible by 4, making it easier to perform calculations and avoid errors.
Science: In scientific calculations, the divisibility rule for 4 can help scientists quickly determine whether a number is divisible by 4, making it easier to perform complex calculations and obtain accurate results.
Finance: In financial calculations, the divisibility rule for 4 can help financial analysts quickly determine whether a number is divisible by 4, making it easier to perform calculations and make informed decisions.

Tips for Applying the Divisibility Rule for 4

Here are some tips for applying the divisibility rule for 4:

Focus on the last two digits: When applying the divisibility rule for 4, focus on the last two digits of the number and check if they form a number that is divisible by 4.
Use mental math: To quickly determine whether a number is divisible by 4, use mental math to calculate the last two digits of the number and check if they form a number that is divisible by 4.
Practice, practice, practice: The more you practice applying the divisibility rule for 4, the more comfortable you will become with using this rule to determine whether a number is divisible by 4.

Conclusion

Q&A: Divisibility Rules for 4

Q: What is the divisibility rule for 4?

A: The divisibility rule for 4 states that a number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Q: How do I apply the divisibility rule for 4?

A: To apply the divisibility rule for 4, focus on the last two digits of the number and check if they form a number that is divisible by 4.

Q: What are some examples of numbers that are divisible by 4?

A: Some examples of numbers that are divisible by 4 include:

12 (last two digits: 12, which is divisible by 4)
24 (last two digits: 24, which is divisible by 4)
36 (last two digits: 36, which is divisible by 4)
48 (last two digits: 48, which is divisible by 4)

Q: What are some examples of numbers that are not divisible by 4?

A: Some examples of numbers that are not divisible by 4 include:

13 (last two digits: 13, which is not divisible by 4)
27 (last two digits: 27, which is not divisible by 4)
35 (last two digits: 35, which is not divisible by 4)
43 (last two digits: 43, which is not divisible by 4)

Q: Can I use the divisibility rule for 4 to check if a number is divisible by 8?

A: No, the divisibility rule for 4 only applies to numbers that are divisible by 4. To check if a number is divisible by 8, you need to use a different divisibility rule.

Q: How do I check if a number is divisible by 8?

A: To check if a number is divisible by 8, you need to use the divisibility rule for 8, which states that a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Q: What are some examples of numbers that are divisible by 8?

A: Some examples of numbers that are divisible by 8 include:

16 (last three digits: 16, which is divisible by 8)
24 (last three digits: 24, which is divisible by 8)
32 (last three digits: 32, which is divisible by 8)
40 (last three digits: 40, which is divisible by 8)

Q: What are some examples of numbers that are not divisible by 8?

A: Some examples of numbers that are not divisible by 8 include:

13 (last three digits: 13, which is not divisible by 8)
27 (last three digits: 27, which is not divisible by 8)
35 (last three digits: 35, which is not divisible by 8)
43 (last three digits: 43, which is not divisible by 8)

Conclusion

In conclusion, the divisibility rule for 4 is an essential tool in mathematics that helps us determine whether a number is divisible by 4 without performing the actual division. By applying this rule, we can quickly determine whether a number is divisible by 4 and perform calculations more efficiently. Whether you are an accountant, scientist, or financial analyst, the divisibility rule for 4 is an essential tool that can help you perform calculations more efficiently and make informed decisions.

Frequently Asked Questions

Q: What is the divisibility rule for 4? A: The divisibility rule for 4 states that a number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Q: How do I apply the divisibility rule for 4? A: To apply the divisibility rule for 4, focus on the last two digits of the number and check if they form a number that is divisible by 4.
Q: What are some examples of numbers that are divisible by 4? A: Some examples of numbers that are divisible by 4 include 12, 24, 36, and 48.
Q: What are some examples of numbers that are not divisible by 4? A: Some examples of numbers that are not divisible by 4 include 13, 27, 35, and 43.

Additional Resources

Divisibility Rules for 2: The divisibility rule for 2 states that a number is divisible by 2 if the number formed by its last digit is even.
Divisibility Rules for 5: The divisibility rule for 5 states that a number is divisible by 5 if the number formed by its last digit is 0 or 5.
Divisibility Rules for 6: The divisibility rule for 6 states that a number is divisible by 6 if the number formed by its last digit is divisible by 2 and 3.