/*! 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 28 Find the prime factorization of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 28

Find the prime factorization of each number. If the number is prime, state this. $$ 54 $$

Short Answer

Expert verified
54 = 2 脳 3鲁.

Step by step solution

01

Identify if the Number is Prime

Determine if 54 is a prime number. Since it is not greater than 1 and cannot only be divided by 1 and itself, it is not a prime number.
02

Start with the Smallest Prime Number

Begin dividing 54 by the smallest prime number, which is 2. 54 梅 2 = 27. This means 54 can be factored as 2 脳 27.
03

Continue Factoring 27

Now, take 27. Since it is not divisible by 2, try the next smallest prime number, which is 3. 27 梅 3 = 9. So now we have the factorization: 54 = 2 脳 3 脳 9.
04

Factor Further if Possible

Next, take 9. Since it is not divisible by 2, use the prime number 3 again. 9 梅 3 = 3, giving us: 54 = 2 脳 3 脳 3 脳 3.
05

Confirm All Numbers are Prime

Now confirm that all the factors (2, 3, 3, 3) are prime numbers. Since each factor is prime, the prime factorization of 54 is complete.

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.

prime numbers
Prime numbers are the building blocks of whole numbers. They are greater than 1 and can only be divided by 1 and themselves without leaving a remainder. For example, 2, 3, 5, and 7 are prime numbers. These special numbers play a crucial role in number theory and are used in various fields like cryptography and computer science.
factorization
Factorization is the process of breaking down a number into smaller numbers that can be multiplied together to give the original number. Think of it like breaking a big problem into smaller, more manageable pieces. For instance, if you have the number 54, you can factor it into 2 脳 27 or 2 脳 3 脳 9, until you get all the smallest building blocks, like 2 脳 3 脳 3 脳 3.
division method
The division method helps in finding the prime factors of a number by dividing it repeatedly by the smallest prime numbers. Here's how you can use it:
鈥� Start with the smallest prime number, which is 2.
鈥� Divide your number (in this case, 54) by 2, and if it divides evenly, write down 2 as a factor and keep the quotient.
鈥� Continue dividing the quotient by 2 until it no longer divides evenly.
鈥� Move to the next smallest prime number (3) and repeat.
鈥� Continue this process until all the factors are prime numbers.
By dividing step-by-step, you ensure that you methodically break down the number into its simplest prime factors.
prime factors
Prime factors are the prime numbers that you multiply together to get the original number. In our example, 54, the prime factors are 2, 3, 3, and 3. So, the prime factorization of 54 is 2 脳 3 脳 3 脳 3. Each of these factors is a prime number, and when multiplied together, they give you 54. Knowing the prime factors of a number is very useful in many areas of mathematics and science.

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

Evaluate using a calculator. $$ \frac{1}{2}(x+5 / z)^{2}, \text { for } x=141 \text { and } z=0.2 $$

Simplify. $$ 5 x^{4}+3 x-\left(5 x^{4}+3 x\right) $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{2.5^{2}-10 \cdot 12 \div(-1.5)}{(3+5)^{2}-60} $$

Simplify. $$ 4 m-9 n+3(2 m-n) $$

Simplify. $$ \frac{-3^{3}-2 \cdot 3^{2}}{8 \div 2^{2}-(6-|2-15|)} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.