Which Of The Following Numbers Is Divisible By 3 And $9$?A) 74,028 B) 40,653 C) 62,997 D) 95,376

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Introduction

In mathematics, divisibility rules are essential tools for determining whether a number is divisible by a specific divisor. In this article, we will explore the divisibility rules for 3 and 9, and apply these rules to determine which of the given numbers is divisible by both 3 and 9.

Divisibility Rule for 3

The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. This rule can be applied to any number, regardless of its size or complexity.

Divisibility Rule for 9

The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. This rule is similar to the rule for 3, but with a higher divisor.

Applying the Divisibility Rules

To determine which of the given numbers is divisible by 3 and 9, we will apply the divisibility rules to each option.

Option A: 74,028

To determine if 74,028 is divisible by 3, we will calculate the sum of its digits:

7 + 4 + 0 + 2 + 8 = 21

Since 21 is divisible by 3, we can conclude that 74,028 is divisible by 3.

To determine if 74,028 is divisible by 9, we will calculate the sum of its digits:

7 + 4 + 0 + 2 + 8 = 21

Since 21 is not divisible by 9, we can conclude that 74,028 is not divisible by 9.

Option B: 40,653

To determine if 40,653 is divisible by 3, we will calculate the sum of its digits:

4 + 0 + 6 + 5 + 3 = 18

Since 18 is divisible by 3, we can conclude that 40,653 is divisible by 3.

To determine if 40,653 is divisible by 9, we will calculate the sum of its digits:

4 + 0 + 6 + 5 + 3 = 18

Since 18 is not divisible by 9, we can conclude that 40,653 is not divisible by 9.

Option C: 62,997

To determine if 62,997 is divisible by 3, we will calculate the sum of its digits:

6 + 2 + 9 + 9 + 7 = 33

Since 33 is divisible by 3, we can conclude that 62,997 is divisible by 3.

To determine if 62,997 is divisible by 9, we will calculate the sum of its digits:

6 + 2 + 9 + 9 + 7 = 33

Since 33 is not divisible by 9, we can conclude that 62,997 is not divisible by 9.

Option D: 95,376

To determine if 95,376 is divisible by 3, we will calculate the sum of its digits:

9 + 5 + 3 + 7 + 6 = 30

Since 30 is divisible by 3, we can conclude that 95,376 is divisible by 3.

To determine if 95,376 is divisible by 9, we will calculate the sum of its digits:

9 + 5 + 3 + 7 + 6 = 30

Since 30 is divisible by 9, we can conclude that 95,376 is divisible by 9.

Conclusion

Based on the divisibility rules for 3 and 9, we have determined that the number 95,376 is the only option that is divisible by both 3 and 9.

Recommendations

  • To determine if a number is divisible by 3 or 9, apply the divisibility rules by calculating the sum of its digits.
  • If the sum of the digits is divisible by 3 or 9, the number is divisible by 3 or 9, respectively.
  • Practice applying the divisibility rules to different numbers to become more confident in your ability to determine divisibility.

Final Thoughts

Introduction

In our previous article, we explored the divisibility rules for 3 and 9, and applied these rules to determine which of the given numbers is divisible by both 3 and 9. In this article, we will answer some frequently asked questions (FAQs) about divisibility rules.

Q: What is the divisibility rule for 3?

A: The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.

Q: What is the divisibility rule for 9?

A: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9.

Q: How do I apply the divisibility rules?

A: To apply the divisibility rules, simply calculate the sum of the digits of the number and check if it is divisible by 3 or 9.

Q: What if the sum of the digits is not divisible by 3 or 9?

A: If the sum of the digits is not divisible by 3 or 9, the number is not divisible by 3 or 9, respectively.

Q: Can I use the divisibility rules for other numbers?

A: Yes, the divisibility rules can be applied to any number, regardless of its size or complexity.

Q: Are there any other divisibility rules?

A: Yes, there are divisibility rules for other numbers, such as 2, 4, 5, 6, 7, 8, 10, and 11. However, the divisibility rules for 3 and 9 are some of the most commonly used and useful rules.

Q: How can I practice applying the divisibility rules?

A: You can practice applying the divisibility rules by trying different numbers and calculating the sum of their digits. You can also use online resources or worksheets to practice applying the divisibility rules.

Q: What are some real-world applications of divisibility rules?

A: Divisibility rules have many real-world applications, such as:

  • Checking if a number is a multiple of a certain divisor
  • Determining if a number is a factor of another number
  • Finding the greatest common divisor (GCD) of two numbers
  • Checking if a number is a perfect square or perfect cube

Conclusion

In conclusion, the divisibility rules for 3 and 9 are essential tools for determining whether a number is divisible by these divisors. By applying these rules, we can quickly and easily determine which numbers are divisible by 3 and 9. We hope that this article has answered some of your frequently asked questions about divisibility rules.

Recommendations

  • Practice applying the divisibility rules to different numbers to become more confident in your ability to determine divisibility.
  • Use online resources or worksheets to practice applying the divisibility rules.
  • Explore other divisibility rules, such as the rules for 2, 4, 5, 6, 7, 8, 10, and 11.

Final Thoughts

In conclusion, the divisibility rules for 3 and 9 are essential tools for determining whether a number is divisible by these divisors. By applying these rules, we can quickly and easily determine which numbers are divisible by 3 and 9. We hope that this article has been helpful in answering some of your frequently asked questions about divisibility rules.