/*! 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 21 Identify each natural number as ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 21

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$140$$

Short Answer

Expert verified
The number 140 is a composite number, and its prime factorization is \(2^2 \times 5^1 \times 7^1 \).

Step by step solution

01

Determining if the number is Prime or Composite

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For 140, it's clearly divisible by numbers other than 1 and itself, like 2, 5, 7, 10, 14, etc. Therefore, 140 is a composite number.
02

Prime factorization

The prime factorization of a number is attained by dividing the original number and its factors by prime numbers until all the factors are prime. For 140, if we initially divide by the lowest prime number, 2, we have two factors: 2 and 70. Breaking 70 down further gives us prime factors 2 and 35. Finally, 35 is broken down into 5 and 7. So, the prime factorization is \(2 \times 2 \times 5 \times 7\), or we can also write it as \(2^2 \times 5^1 \times 7^1 \).

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!

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

In Exercises \(89-92,\) express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Subtract 11 from \(9 .\) Multiply this difference by \(2 .\) Raise this product to the fourth power.

Write a positive or negative integer that describes each situation. Navigation: 65 feet above sea level

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$8^{2}-16 \div 2^{2} \cdot 4-3$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. nine increased by the product of 3 and 2 less than a number

Simplify: \(-8-2-(-5)+11 .\) (Section 1.6, Example 3)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.