Common Factors ang Grouping

Today, lesson want about Common factors and grouping.

The object of these are:

·         Find the greatest common factor (GCF) of the numbers

·         Find the greatest common factor (GCF) of the terms

·         Factor out the greatest common factor

·         And then finally, factor a four term expression by grouping

So, lets get study with some definition in particular product and factor.

Let say we have many expressions

Fifteen equals three  times five.

We say that fifteen is the product and the factors are three and five.

What we mean by factoring is that factoring completely means to have all factors as prime number.

The key is we have fifteen broken down as factors three and five.

Another expression is twenty that brokrn in to the prime numbers of two times two times five. This number can not be broken down any further.

To find the greatest common factor of number, we are provided with the list of the integers. In the list, the  largest  common factor of integers is noun as the  greatest common factor.

So, lets taken example:

Fourty five  can be broken down in to three times three times five or three square times five.

Another number is sixty.  Sixty can be broken down as two square times three times five.

You know that three square times five equals fourty five. Three square is nine, nine times five is fourty five.

Two square is four.Four times three is tweleve. Tweleve times five is sixty.

·         To find the greatest common factor, choose prime nombers. Fourty five have two factors and sixty is three factors here. Choose prime factors with the smallest exponents and find their product.

So the common here is three, the smallest exponent is one. The common here also is five and the smallest exponent is also one.

Therefore three and five are common factors of fourty five and sixty. Now we can say that three times five equals fifteen.  Therefore, fifteen is the greatest common factor between fourty five and sixty.

Once again, to finding the greatest common factor of numbers, we find the smallest exponent  and choose the sadow of prime factors and then find their product.

So, lets consider thirty six, sixty, and one hundred and eight.

Thirty six can be broken down as wo square times three square. We know that two square is four and three square is nine. So four times nine is thirty six.

Like that ways, we have sixty. Sixty can be broken down as two square times three times five. Two square is four, Four times three is tweleve and tweleve times five is sixty, and finally we had the number of one hundred eight wich we can broke down as two square times three cube is twenty seven. Four times twenty seven is one hundred eight.

We can see here two is common among of this numbers and the exponent is two. So, two square is one of the prime factors.

Three is the common of this numbers and the smallest exponent is one. Therefore, we have two square times three. Now that two square is the smallest with the base two and three is has exponents of one. Its common and smallest exponent are associated. So, tweleve is the greatest common factor among thirty six, sixty, and one hundred and eight.

Another way is to doing this is:

We can take thirty six,sixty and one hundred and eighty and We devide two among that. So, therefore we know that thirty six divide by two is eighteen, sixty divide by two is thirty, and one hundred and eight divide by two is fivety four. Again we can divide by two. So, this is eighteen divide by two is nine, thirty divide by two is fifteen, and fivety four divide by two is twenty seven. See that it is three  common among them. So, we have here nine divide by three is three, fifteen divide by three equals five, and twenty seven divide by three is nine. We can see that it is can not be broken down to any factors. So, what we have here is collect this term here two two three. We get same result using this approach.