/*! 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 140 Find all the factors of the numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 140

Find all the factors of the number. $$13$$

Short Answer

Expert verified
The factors of 13 are only 1 and 13

Step by step solution

01

Identify the Number

We are asked to find the factors of the number 13.
02

Determine if the number is a Prime

As 13 is a prime number, it can only be divided evenly by 1 and itself, which is 13. There are no other factors of 13.

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.

Factors
Factors are numbers that divide another number completely without leaving a remainder. To find the factors of a number, you only need to look at the numbers that fit evenly into it. When we talk about factors, we often use the idea of multiplication:
  • If you can multiply two whole numbers to get the target number, those two numbers are factors.
For example, suppose you want to find the factors of 6. You can list them as:
  • 1 and 6, because 1 x 6 = 6
  • 2 and 3, because 2 x 3 = 6
The number 13 is a bit different because it is a prime number. It's only factors are 1 and 13. This makes it unique compared to numbers like 6, which has more than two factors.
Divisibility
Divisibility takes us a step deeper into understanding factors. A number is divisible by another if, after division, the remainder is zero. We see this because divisibility tests if one number is an exact multiple of another.
For example:
  • 15 is divisible by 3 because 15 梅 3 = 5, with no remainder.
  • 20 is divisible by 5 because 20 梅 5 = 4, with no remainder.
Applying this concept, since 13 is a prime number, it is only divisible by 1 and itself. Trying to divide 13 by any number other than 1 and 13 will always leave a remainder. Hence, 13 passes the test for divisibility only with 1 and 13.
Integers
Integers are the set of whole numbers that can be positive, negative, or zero. They do not have fractions or decimal parts.
  • Examples of integers are -3, 0, 4, and 15.
Factors, divisibility, and prime numbers all revolve around these whole numbers. The concept of integers is essential to understand when working with factors because factors must be integers. When we say 13 is a prime number with factors, we specifically mean positive integer factors, which are only 1 and 13.
The role of integers in mathematical concepts like factors represents stability and predictability in equations and calculations.
Prime Factorization
Prime factorization involves breaking down a number into its simplest building blocks, called prime numbers. Prime numbers are numbers that have only two factors: 1 and the number itself. Think of them as the atoms of mathematics, representing the basics from which we build other numbers.
  • For example, the number 28 can be broken into prime numbers as 2 x 2 x 7.
In the case of the number 13, its prime factorization is unique. Since 13 is a prime number itself, it cannot be broken down further. Therefore, its prime factorization is simply 13.
Prime factorization is an essential aspect of number theory and helps solve more complex mathematical problems by enabling simpler calculations with prime numbers.

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

Geometry Find a. the perimeter and b. the area of a rectangle with a length of \(24 \mathrm{m}\) and a width of \(15 \mathrm{m}\)

Represent the sum of 5 and 4 using arrows on a number line.

Divide. $$8947 \div 223$$

Loans Find the total amount paid on a loan when the monthly payment is 187$ and the loan is paid off in 36 months. Use the formula A=M N, where A is the total amount paid, M is the monthly payment, and N is the number of payments.

Prime Numbers a. All prime numbers greater than 10 end in one of four digits. What are those digits? b. A number that ends in one of the digits in part (a) is not necessarily a prime number. For each digit in part (a), give an example of a number that ends in that digit but is not a prime number.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision 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.