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What factors do 28 and 44 have in common?

umka21 [38]

2 and 9 are factors of 18.

When we have two or more given numbers, we can find the largest factor that both numbers have in common. This is called the GCF or the Greatest Common Factor.

There are several different methods that can be used to find the GCF. Let's take a look at some of the methods.

Method 1: List out the factors.

Example: Find the GCF of 64 and 96. 

Step 1: List the factors of each number. 

64: 1, 2, 4, 8, 16, 32, 64

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Step 2: Look for factors that both lists have in common.

Step 3: Pick out the largest factor that both lists have in common and call this the GCF.

Therefore, the GCF of 64 and 96 is 32.

Method 2: Upside Down Division

Find the GCF of 280 and 144.

Step 1: Place the numbers inside an upside down division bar.

Step 2:Now, we need to divide both numbers by a common factor. Because both of the numbers are even, we could start with 2.The answer goes underneath the bar.

Step 3: We will continue to divide until we have two numbers that are relatively prime. Remember that relatively prime means two numbers that do not have any common factors other than 1.

35 and 18 are relatively prime. 

Step 4: Now we take all of the factors on the side and multiply them together.

6 0

3 years ago

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In this task, you will perform multiplication on rational and irrational numbers and determine whether the sets are closed under

velikii [3]

Answer:

The set of rational numbers is closed under multiplication.

The set of irrational numbers is not closed under multiplication.

Although are only few instances where the set of irrational numbers may show closure, but it must be noted that closure property would not extend to the entire set of irrational numbers.

The Product of two rational numbers will be rational.

Step-by-step explanation:

The set of rational numbers contains the set of numbers that can be written as a fraction or ratio between two integers - integer values in the nominator and denominator (denominator ≠ 0).

The set of integers - denoted by Z - can be termed as rational numbers as integer, for instance, 3 can be written as the ration 3/1.

Therefore, when we multiply two rationals, it basically means we are just multiplying two such fractions which will yield another fraction of the same form as integers are closed under multiplication.

Part A) Determining multiplication on rational numbers

Let a/b and c/d be rational numbers where a, b, c and d are integers and (b, d ≠ 0).

For example, a = 2, b = 3, c = 4, and d = 5 a, b, c and d are integers

Lets multiple 2/3 × 4/5 to check what the multiplication of two rational number can bring.

So,

2/3 × 4/5 = (2)(4) / (3)(5) = 8/15

As 8 and 15 are the integers, and can be written in a ratio 8/15 in the nominator and denominator which make it a rational number. Hence, the set of rational numbers is closed under multiplication.

Determining multiplication on irrational numbers

The set of irrational numbers contains the set of numbers that can not be written as a fraction or ratio between two integers.

The product of two irrational numbers will be sometimes irrational.

There will be certain cases sometimes where the product of two irrational numbers will yield irrational number. But, it must be noted that few irrational numbers may multiply to yield a rational number.

For example,

√5 × √2 = √10 which is termed as irrational

√8 × √2 = √16 = 4 which is termed as rational

So, there are only few instances that may show closure, but it must be noted that closure property would not extend to the entire set of irrational numbers.

So, we can safely say that the set of irrational numbers is not closed under multiplication.

Part B) Is the Product of two rational numbers irrational or rational?

Let a/b and c/d be rational numbers where a, b, c and d are integers and (b, d ≠ 0).

Lets multiple a/b × c/d to check if the product of two rational numbers can be rational or irrational.

So,

a/b × c/d = ac / bd where b, d ≠ 0

As ac and bd are also integers, so the sets are closed under multiplication.

So, ac/bd is a ratio having integers in the nominator and denominator which make it a rational number. Hence, the Product of two rational numbers will be rational.

Proving closure property

Let x and y are rational numbers such that

x = a/b and y = c/d where b, d ≠ 0 and a, b, c and d are integers

x × y = a/b × c/d

xy = ac / bd

As ac and bd are also integers, so the sets are closed under multiplication.

So, ac/bd is a ratio having integers in the nominator and denominator which make it a rational number. Hence, the product of two rational numbers will be rational.

For example,

x = a/b = 6/7

y = c/d = 8/9

xy = a/b × c/d

xy = ac / bd = (6)(8) / (9)(7)

xy = 48/63

As 48 and 63 are the integers, and can be written in a ratio 48/63 in the nominator and denominator which make it a rational number. Hence, the set of rational numbers is closed under multiplication.

Keywords: closure property, rational number, irrational number

Learn more about closure property and rational number from brainly.com/question/7667707

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4 0

3 years ago

David was 3 when Marieka was born. David is 32 now, how old is Marieka?

Alex777 [14]

Answer:

Marieka will be 3 years younger that David

Step-by-step explanation:

she'll be 29 years old ...

7 0

3 years ago

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A number less than 85 the number has 26 and 6 as factors

Len [333]

A number that is less than 85, the number has 26 and 6 as factors is, 78

7 0

3 years ago

What is the total cost of a $2,099 couch including the 6.5% sales tax?

fomenos

Answer:

$2422

Step-by-step explanation:

2099/6.5=322.923076923 (were rounding that to 323)

so 2099+323=2422

8 0

3 years ago

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