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Chapter 1: Problem 26

Which of the following numbers is not divisible by 3? $$325, 501, 945, 381$$

Short Answer

Expert verified
325 is not divisible by 3.

Step by step solution

01

Understand the Divisibility Rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3. We will apply this rule to each of the four given numbers.
02

Check Divisibility for 325

Add the digits of 325: \(3 + 2 + 5 = 10\). Since 10 is not divisible by 3, 325 is not divisible by 3.
03

Check Divisibility for 501

Add the digits of 501: \(5 + 0 + 1 = 6\). Since 6 is divisible by 3, 501 is divisible by 3.
04

Check Divisibility for 945

Add the digits of 945: \(9 + 4 + 5 = 18\). Since 18 is divisible by 3, 945 is divisible by 3.
05

Check Divisibility for 381

Add the digits of 381: \(3 + 8 + 1 = 12\). Since 12 is divisible by 3, 381 is divisible by 3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Divisibility by 3
Being able to determine if a number is divisible by 3 is a simple yet powerful tool in arithmetic. The "divisibility by 3" rule is based purely on the sum of a number's digits. Here's how it works:

  • If the sum of a number's digits is divisible by 3, then the number itself is also divisible by 3.
  • If the sum is not divisible by 3, the number is also not divisible by 3.
This rule offers a quick way to see if a large number can be divided by 3 without leaving a remainder, thereby making it handy in various mathematical and real-world calculations.
Sum of Digits
The concept of the "sum of digits" is foundational in understanding divisibility rules. It involves adding up all the individual digits in a number.

Here's why it's useful:
  • When checking divisibility by 3, adding the digits can save you from doing more complex division calculations.
  • It simplifies large numbers into smaller, more manageable computations.
  • This method reduces errors as you break down problems into smaller parts.
Consider the number 945. By adding the digits 9, 4, and 5, you get 18. Since 18 is divisible by 3, 945 is also divisible by 3. This technique applies universally, regardless of how large the number may seem.
Mathematics Problem-Solving
Problem-solving in mathematics often involves using clever little tricks like the divisibility rules. It empowers students with strategies that simplify complex tasks:

  • Approaching large numbers can be intimidating, but understanding key concepts brings clarity and confidence.
  • Using rules like divisibility by 3 ensures you can quickly narrow down your options and focus on finding solutions.
Remember, mathematics is not only about finding the answer but also about understanding the "why" and "how" of the process. This mindset makes problem-solving not just a skill-set but a way to approach challenges in everyday life with ease and logic.

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Most popular questions from this chapter

Simplify the given expression. $$ 7 \cdot[8-5]-10 $$

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