Factoring Algebra

posted on: 06 Mar, 2012 | updated on: 22 Sep, 2012

Math factoring is very much useful in almost all the fields of mathematics. In factoring Algebra, factors are any algebraic expression which divides another algebraic expression where the remainder is zero. Similarly in case of Numbers we use numbers instead of algebraic expressions.For instance: 4 and 2 are the factors of 8 which means that both the numbers divides 8 completely as 8 ÷ 2 = 4 and 8 ÷ 4 = 2.

We can also define factors as the numbers which we multiply so that we can get other number. For example factors of 12 are 3 and 4, because 3*4 = 12. Some numbers may have many factors. Example is 16 can be factored as 1*16, 2*8, or 4*4.

The number which can only be factorized as 1 and itself then that number is called prime number. For example 2, 3, 5, 7, 11, 13 . . . . are the Prime Numbers. The number 1 is always ignored in case of Factorization because it comes always in almost everything and it do not considered as a prime number.

The factorization of prime numbers does not include 1. It includes all the copies of each and every prime factor. For example: Prime factorization of 8 = 2*2*2 that is not only 2. Here 2 is the only factor of 8 but it is not sufficient means we need three copies of 2 so if we multiply 2 by itself 3 times we get back 8; therefore the prime factorization of 8 includes 3 copies of 2.

Again if we look at the prime factorization it will only consider the prime factors not the products of those factors. For example: 2*2 is 4 and 4 is a divisor of 8 but 4 is not considered as a prime factor of 8. Because 8 is not equal to 2*2*2*4.

Suppose in factoring Math the task is to get the prime factorization of 24. Now if we only collect all the divisors of 24 as 1, 2, 3, 4, 6, 8, 12, and 24 and we multiply all the divisors of 24 as 1*2*3*4*6*8*12*24 will result in 331776 which are not 24 so it is not the right way. So we use prime factorization, either the problem needs it or not to avoid such over duplication or multiplication. So for this we can find the prime factor of 24 by dividing 24 by the smallest prime number which is 2 i.e. 24 / 2 = 12. Now again divide the result 12 by the smallest prime number 2 as 12 / 2 = 6; again divide 6 by 2 as 6 / 2 = 3 and here we get a prime number that is 3 so we do not need to further divide this because the prime numbers has factors 1 and itself; so we are done. So the factors of 24 are 2, 2, 2 and 3.

Find the prime factor of 1008

Solution:

1002 ÷ 2 = 504

504 ÷ 2 = 252

252 ÷ 2 = 126

126 ÷ 2 = 61

So it has solution 1002 = (504) (252) (126) (61).

Topics Covered in Factoring Algebra

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