/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 The number 126 is divisible by w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 2

The number 126 is divisible by which of the following? a. 2 b. 3 c. 5 d. 10

Short Answer

Expert verified
126 is divisible by 2 and 3.

Step by step solution

01

Check divisibility by 2

A number is divisible by 2 if its last digit is even. The last digit of 126 is 6, which is even. Thus, 126 is divisible by 2.
02

Check divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3. The digits of 126 are 1, 2, and 6. Find the sum: 1 + 2 + 6 = 9. Since 9 is divisible by 3, 126 is also divisible by 3.
03

Check divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. The last digit of 126 is 6, which is neither 0 nor 5. Therefore, 126 is not divisible by 5.
04

Check divisibility by 10

A number is divisible by 10 if its last digit is 0. The last digit of 126 is 6. Therefore, 126 is not divisible by 10.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Divisibility by 2
Divisibility by 2 is perhaps the simplest rule. A number is divisible by 2 if its last digit is an even number. Even numbers end in 0, 2, 4, 6, or 8.
  • Examples: 14, 26, 38, 50 are all divisible by 2 because their last digits are 4, 6, 8, and 0 respectively.
  • Non-examples: 15, 27, 39, 51 are not divisible by 2 because their last digits are 5, 7, 9, and 1 respectively.
In the case of 126, the last digit is 6, which is even. Therefore, 126 is divisible by 2.
Divisibility by 3
Divisibility by 3 requires a bit more work but is still quite simple. To determine if a number is divisible by 3, sum up all its digits. If the sum is divisible by 3, then the original number is too.
  • Examples: For 123, the sum of the digits is 1 + 2 + 3 = 6. Since 6 is divisible by 3, 123 is also divisible by 3.
  • Non-examples: For 124, the sum of the digits is 1 + 2 + 4 = 7. Since 7 is not divisible by 3, 124 is also not divisible by 3.
For the number 126, you sum the digits: 1 + 2 + 6 = 9. Since 9 is divisible by 3, the number 126 is also divisible by 3.
Divisibility by 5
The rule for divisibility by 5 is quite straightforward. A number is divisible by 5 if its last digit is either 0 or 5.
  • Examples: 20, 35, 50 are divisible by 5 because their last digits are 0 or 5.
  • Non-examples: 21, 36, 52 are not divisible by 5 because their last digits are 1, 6, and 2 respectively.
Looking at 126, the last digit is 6. Since 6 is neither 0 nor 5, 126 is not divisible by 5.
Divisibility by 10
Divisibility by 10 is the easiest to check. A number is divisible by 10 if its last digit is 0.
  • Examples: 20, 30, 100 are all divisible by 10 because their last digits are 0.
  • Non-examples: 21, 31, 101 are not divisible by 10 because their last digits are 1.
For the number 126, the last digit is 6. Since 6 is not 0, 126 is not divisible by 10.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write three fractions equivalent to \(-\frac{12}{18}\)

Convert the improper fraction to a mixed number. $$\frac{52}{9}$$

Label the fraction as proper or improper. $$\frac{7}{2}$$

Divide. Write the quotient as a mixed number. $$7213 \div 8$$

Simplify the fraction to lowest terms. Write the answer as a fraction or a whole number. $$\frac{85}{153}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.