Problem 4 Determine whether the second num... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 2: Problem 4

Determine whether the second number is a factor of the first. $$ 680 ; 16 $$

Short Answer

Expert verified

16 is not a factor of 680.

Step by step solution

Understand the concept of factoring

A number is a factor of another number if it divides that number exactly without leaving a remainder. In this case, we need to determine if 16 is a factor of 680.

Set up the division

To see if 16 is a factor of 680, set up the division of 680 by 16. We need to calculate $ \frac{680}{16} $.

Perform the division

Divide 680 by 16. Calculate $ \frac{680}{16} = 42.5 $.

Analyze the result

Since the result of the division $ \frac{680}{16} $ is 42.5 and not an integer, 16 does not divide 680 exactly. Therefore, 16 is not a factor of 680.

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Key Concepts

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

Division

Division is one of the four basic operations in arithmetic. It lets us split numbers into equal parts. When you divide one number by another, you are looking to see how many times the second number fits into the first.
In our example, we are dividing 680 by 16. The question is: How many times does 16 fit into 680? We perform the division $ \frac{680}{16} $.
After doing the math, we find that 16 fits into 680 exactly 42.5 times. This means that 16 does not fit into 680 perfectly since division leaves us with a fractional number.

Remainder

When you perform division, sometimes the second number does not fit perfectly into the first number. This leaves us with what's called a 'remainder'.
For instance, if we divide 10 by 3, we get 3 with a remainder of 1, because 3 fits into 10 three times (9) and leaves us with 1 left over. However, in the division of $ \frac{680}{16} $, our result was 42.5 with no remainder we'd consider for whole integers.
This is important because in order for the second number to be considered a factor of the first, the remainder after division should be zero.
In our specific problem, since dividing 680 by 16 does not yield an exact whole number, we know that 16 is not a factor of 680.

Integers

Integers are whole numbers that can be positive, negative, or zero. Examples of integers are -3, 0, 1, 42, etc.
When we talk about factoring and performing divisions, we are ideally looking to see the division results in an integer. This means there would be no fraction or decimal part left in the answer.
In the division $ \frac{680}{16} $, the answer is 42.5, a decimal number, not an integer. This confirms that 16 does not divide 680 perfectly, further proving that 16 is not a factor of 680.

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91影视

Determine whether the second number is a factor of the first. $$ 680 ; 16 $$

Short Answer

Step by step solution

Understand the concept of factoring

Set up the division

Perform the division

Analyze the result

Key Concepts

Division

Remainder

Integers

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