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Chapter 1: Problem 60

Which of the following numbers is not divisible by 8? $$3312, 1736, 9338, 3912$$

Short Answer

Expert verified
9338 is not divisible by 8.

Step by step solution

01

Understand Divisibility by 8

A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8. We'll check the last three digits of each option given.
02

Check 3312

The last three digits of 3312 are 312. Divide 312 by 8. \[312 \div 8 = 39\]39 is a whole number, so 312 is divisible by 8. Hence, 3312 is divisible by 8.
03

Check 1736

The last three digits of 1736 are 736. Divide 736 by 8. \[736 \div 8 = 92\]92 is a whole number, so 736 is divisible by 8. Hence, 1736 is divisible by 8.
04

Check 9338

The last three digits of 9338 are 338. Divide 338 by 8.\[338 \div 8 = 42.25\]42.25 is not a whole number, so 338 is not divisible by 8. Hence, 9338 is not divisible by 8.
05

Check 3912

The last three digits of 3912 are 912. Divide 912 by 8.\[912 \div 8 = 114\]114 is a whole number, so 912 is divisible by 8. Hence, 3912 is divisible by 8.

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Key Concepts

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

Divisibility by 8
Understanding divisibility by 8 can be simple with a fun little rule. Focus on the last three digits of a number, and if these digits can be divided by 8 without leaving a remainder, then the whole number is divisible by 8. This neat shortcut saves time in various mathematics problems.
Let's dive into an example:
  • Take the number 312 from 3312.
  • Divide 312 by 8, and if the result is a whole number, 3312 is divisible by 8.
  • The division gives 39, which is a whole number, confirming divisibility.
This method simplifies verifying divisibility by 8, especially with lengthy numbers.
Whole Numbers
Whole numbers are numbers without any fractional or decimal part. They include zero and all positive numbers. Whole numbers are crucial in determining divisibility because if a division results in a whole number, it means there's no remainder.
For instance, in our divisibility test for solving mathematical problems:
  • 312 divided by 8 equals 39, a whole number.
  • This implies the division was exact.
  • Thus, confirming the number belongs to the set divisible by 8.
This understanding helps ensure calculations are accurate and aligns with mathematical rules of divisibility.
Mathematics Problems
Mathematics problems often involve recognizing and applying concepts like divisibility to find solutions. Solving these problems requires breaking them into manageable steps using clear rules.
By understanding problems deeply, like identifying if a number is divisible by 8, solutions become more achievable.
  • Check the last three digits of the number.
  • Perform the division and observe the outcome.
  • If there鈥檚 no remainder, mark it as divisible.
This logical approach eases solving complex mathematical exercises and enhances learning efficiency.

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Most popular questions from this chapter

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