/*! 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 16 8 is a factor of 98... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

8 is a factor of 98

Short Answer

Expert verified
8 is not a factor of 98.

Step by step solution

01

Understand the Problem

A factor is a number that divides another number evenly without leaving a remainder. We need to determine whether 8 divides 98 evenly.
02

Set Up the Division

We need to divide 98 by 8, which means we perform the division 98 梅 8.
03

Perform the Division

Carry out the division by dividing 98 by 8. 1. 8 goes into 98 twelve times because 8 脳 12 = 96, getting close to but not exceeding 98. 2. Subtract 96 (8 脳 12) from 98 to find the remainder. 3. 98 - 96 = 2, so there is a remainder of 2.
04

Analyze the Result

Because the division of 98 by 8 gives a remainder of 2, 8 is not a factor of 98. A number can only be a factor if it divides the other number with a remainder of 0.

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.

Understanding Division
Division is a fundamental operation in mathematics. It helps us understand how many times one number can be grouped into another. In the exercise, you needed to divide 98 by 8 to see if there is no remainder. This checks if 8 is a factor of 98. The process of division in step-by-step involves:
  • Determining how many times the divisor (8) can "fit" into the dividend (98).
  • Performing the division operation, i.e. 98 梅 8.
You see, division breaks down a dataset or number into smaller, equal parts. If you perform the division, 8 goes into 98 exactly twelve times, but it doesn鈥檛 fit perfectly, leaving a small remainder. This is why the concept of remainder is crucial in factoring.
Exploring Remainders
Remainders help us find out what's left after division. They are essential in determining if one number is a factor of another. When you divide 98 by 8, 8 fits 12 whole times into 98, with 2 left over. Hence, 2 is the remainder.
Whenever you have a remainder that is not zero, it simply means the divisor cannot divide the dividend evenly. For instance, here, because the remainder is 2, this tells us 8 is not a factor of 98, as factors require a remainder of zero for complete division. Remember:
  • No remainder (remainder = 0) means the divisor is a factor.
  • Positive remainder (in this case, 2) means the divisor is not a factor.
This tiny leftover value plays a big role in factor determination.
Introducing Multiplication in Factoring
Multiplication is closely connected to division when exploring factors. It is essentially the opposite operation. Let's connect multiplication with the exercise: when we say 8 fits into 98 twelve times, we actually mean multiplying 8 by 12 gives us a product close to 98, precisely 96. This was detailed in the process:
  • You multiplied 8 x 12 to find the largest possible product of 8 that doesn鈥檛 exceed 98.
  • If 8 multiplied by any integer equaled 98, then 8 would be a factor.
Remember:
  • Division finds how one number is a part of another.
  • Multiplication verifies that relation by seeing the product (result of multiplication) aligns with the original number or falls short with a remainder left.
      • When multiplying doesn't match exactly with the number you鈥檙e dividing into, you have your sure sign there's a remainder.

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

Simplify each algebraic expression by combining similar terms. $$5(x-4)+6(x+8)$$

Simplify each algebraic expression by combining similar terms. $$4 m+m-8 m$$

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$59(36)+59(64)$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((a+b)-(a-b)\) for \(a=-16\) and \(b=14\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(2(x+y)-3(x-y)\) for \(x=-2\) and \(y=7\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.